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Conservation Laws
Conservation Laws
Conservation laws in Physics can give
explanations as to why some things occur
and other do not.
Three very important Conservation Laws are:
I.
Conservation of Energy
II.
Conservation of Momentum
III. Conservation of Charge
Energy Conservation (I)
There are many forms of energy.
For now, we’ll focus on two types
1. Kinetic Energy (KE) – Energy of motion
KE = ½ mv2 if v is much less than c (v << c)
2. Mass Energy
m = mass
c = speed of light
= 3x108 [m/sec]
E = mc2
That is, mass is a form of energy, and the “conversion” is to just
multiply the mass by a constant number (the speed of light squared)!
Conservation of Energy (II)
Total Energy (initially)
= ED
= mDc2
D
Suppose D “decays” into 2 particles A and B, what is the energy of
the system afterward?
vA
A
B
vB
Total Energy (after decay)
=
EA
+
EB
= (KEA+mAc2) + (KEB+mBc2)
Since energy must be conserved in the “decay” process,
mDc2 = (KEA+mAc2) + (KEB+mBc2)
Conservation of Energy (III)
mDc2 = (KEA+mAc2) + (KEB+mBc2)
ED
Before
Decay
EA
EB
After Decay
Important points here:
1) This equation DOES NOT say that kinetic energy is conserved
2) This equation DOES NOT say that mass is conserved
3) This equation states that the total energy is conserved
è Total energy before decay = Total energy after decay
Conservation of Energy (IV)
mDc2 = (KEA+mAc2) + (KEB+mBc2)
KEA = ½ mAvA2
>0
KEB = ½ mBvB2 > 0
Since mA and mB must be larger than zero, and vA2>0 and vB2>0,
the KE can only be positive (KE cannot be negative!)
If I subtract off the KE terms from the RHS* of the top equation, I
will no longer have an equality, but rather an inequality:
mDc2 … mAc2 + mBc2
and dividing both sides by c2,
mD … mA + mB
This is also true if
particle D has KE>0
also!
Conservation of Energy (V)
KEA
MAc2
MBc2
KEB
MDc2
LHS = RHS
MAc2
MBc2
MDc2
LHS > RHS
Energy Conservation (VI)
Consider some particle (call it “D”) at rest which has a mass of 0.5 kg
D
Which of the following reactions do you think can/cannot occur?
I
A
D
B
mB=0.1 kg
mA=0.2 kg
II
A
D
B
mA=0.2 kg
mB=0.4 kg
III
A
mA=0.49 kg
IV
A
B
D
D
B
mB=0.0 kg
mA=0.1 kg
mB=0.1 kg
Energy Conservation (VII)
A particle (q) and an anti-particle (q) of equal mass each having
1 [TeV] of energy collide and produce two other particles
t and t (of equal mass) as shown in Fig. A. (1 [TeV] = 1012 [eV])
Fig. A
t
q
Bam
t
q
Energy Conservation (VIII)
q What is the total energy in the collision ?
A) 0
B) 2 [TeV]
C) 1 [TeV] D) 0.5 [TeV]
q What is total energy of the t and t (individually)?
A) 0
B) 2 [TeV]
C) 1 [TeV] D) 0.5 [TeV]
q What can be said about the mass energy of the “t” particle ?
A) It’s equal to the mass of “q”
B) It must be less than 0.5 TeV
C) It must be less than 1 [TeV]
D) It’s equal but opposite in
direction to that of the t
particle
Momentum Conservation (I)
Momentum (p) = mass x velocity = mv
p = mv
Momentum has a direction, given by the direction of v
m1
v1
p2 = -m2v2
p1 = m1v1
v2
m2
Note that particles moving in opposite directions have momenta
which are opposite sign!
Momentum Conservation: In any process, the value of the total
momentum is conserved.
Momentum Conservation (II)
Consider a head-on collision of two particles
m1
v1
v2
m2
What is the total momentum before the collision ?
A) m1v1+m2v2
B) m1v2-m2v1
C) zero
D) (m1+m2)(v1+v2)
If m1= m2, what can be said about the total momentum?
A) it’s zero
B) it’s positive
C) it’s negative D) can’t say?
If m1= m2 and v1 > v2, what can be said about the total momentum?
A) it’s zero
B) it’s positive
C) it’s negative D) can’t say?
Momentum Conservation (III)
Consider a head-on collision of two particles
m1
v1
v2
m2
If m1< m2 and v1 > v2, what can be said about the total momentum?
A) it’s zero
B) it’s positive C) it’s negative
D) can’t say?
If m1= m2 and v1 = v2 (in magnitude), what can be said about the total
momentum?
A) it’s zero
B) it’s positive C) it’s negative
D) can’t say?
In this previous case, what can be said about the final velocities of
particles 1 and 2 ?
A) their zero
B) equal and opposite
C) both in the same direction
D) can’t say?
Momentum Conservation (IV)
Consider a particle D at rest which decays into two lighter particles
A and B, whose combined mass is less than D.
I
vA
A
D
mA
mB
B
vB
If mA > mB, answer the following questions:
q What can be said about the total momentum after the decay?
A) Zero
B) Equal and Opposite
C) Equal
D) Opposite, but not equal
q If mA= mB, what can be said about the magnitudes of the
velocities of A and B?
A) vA>vB
B) Equal and Opposite
C) vB>vA
D) Same direction but different magnitudes
Momentum Conservation (V)
I
vA
A
D
mA
mB
B
vB
q Which statement is most accurate about the momentum of A ?
A) Zero
B) Equal to B
C) Equal and opposite to B
D) Opposite, but not equal
q Can mA+mB exceed mD ?
A) Not enough data
C) No
B) Yes, if vA and vB are zero
D) Yes, if vA and vB are in opposite
directions
Momentum Conservation (VI)
p
mP
e me
n
ν
Consider a neutron, n,
which is at rest, and then
decays.
mp+me < mn
Can this process occur?
a) No, momentum is not conserved
b) Yes, since mn is larger than the sum of mP and me
c) No, energy cannot be conserved
d) Yes, but only between 8 pm and 4 am
The observation that momentum was not conserved in neutron decay lead to the
profound hypothesis of the existence of a particle called the neutrino
neutron à proton + electron + neutrino
(n
à p + e
+
ν)
When the neutrino is included, in fact momentum is conserved.
Discovery of the Neutrino
p
mP
e me
n
ν
The observation that momentum conservation appeared to be
violated in neutron decay lead to the profound hypothesis of the
existence of a particle called the neutrino
neutron à proton + electron + neutrino
(n
à
p + e
+
ν)
When the neutrino is included, in fact momentum is conserved.
Charge Conservation
The total electric charge of a system does not change.
Consider the previous example of neutron decay:
Charge
n
0
à
p
+1
+
e
-1
ν
0
+
Can these processes occur?
p + p
Charge
+1
+1
p + e
Charge
+1
0
0
p
+
+1
à
-1
n + n
Charge
à
ν
0
+
0
à
p
+1
n
n
0
+
NO
YES
p
+1
NO
Summary of Conservation Laws
q Total Energy of an isolated system is conserved
D à A+B
cannot occur if mA+mB > mD
q Total momentum of an isolated system is conserved
- missing momentum in neutron decay signaled the existence
of a new undiscovered particle
q Total Charge of an isolated system is conserved
- the sum of the charges before a process occurs must be the
same as after the process
We will encounter more conservation laws later which will help explain
why some processes occur and others do not.
Matter and energy
“Mass and energy are two different aspects of the same thin
Atoms
An atoms, a basic unit of matter, is a packet of energy with el
The Vibration of Matter
he energy contained in atoms and molecules makes them vibrate a
this vibration produces heat. Matter expands with heat.
Plasma
n a gas atom like hydrogen, when the vibration increases the hea
makes the atom expand more and lose its electron.
Thanks
for
Attention!
Clause
Types … and …
Independent
& Dependent
Let’s start with a simple sentence…
I bought a book.
This sentence has the three basic elements required of either a
simple sentence or a clause:
Subject = I
Verb = bought
Object = a book
Now, let’s add another clause …
While
herher
coffee,
I bought
Whilemy
mymother
motherdrank
drank
coffee,
I
abought
book. a book.
Now we have a two clause sentence, but these clauses are not the same.
The original clause I bought a book can stand on its own as a
simple sentence. It expresses a complete thought by itself. Therefore, it is
called an independent clause.
Independent Clause (IC)
An independent clause is a S + V / O bject
or C omplement
or A dverbial
unit that expresses a complete thought and could stand on its own as a
simple sentence.
Whether you find an independent clause by itself as a simple sentence
or joined with other clauses, you will be able to identify it because
it:
– is a S+V/ unit that
– expresses a complete thought
But what about the other clause?
While my mother drank her coffee, I
bought a book.
If we only consider the first clause, while
my mother drank
her coffee, we are left with a question in our minds, “What
happened while your mother drank her coffee?!”
This clause can not stand on its own as a simple sentence. It requires
another clause to a complete its meaning. Therefore, it is called an
dependent clause.
Dependent Clause (DC)
A dependent clause is a S + V / O bject
or C omplement
or A dverbial
unit that does not express a complete thought and can not stand on
its own as a simple sentence.
A dependent clause must always be connected to an independent
clause. You will be able to identify it because it:
– is a S+V/ unit that
– does not express a complete thought on its own
Dependent Clauses
There are 3 different types of dependent clauses.
• Noun Clause (NC)
• Adjective Clause (AdjC)
• Adverb Clause (AdvC)
Noun Clause (NC)
• [S+V/] that acts like a noun
I think
[you
sick].
• Example: I think
[you
areare
sick].
S
V
O
Objects are nouns; this entire clause acts
like a singular noun, so it is a noun
clause.
• NCs usually follow verbs as objects or complements
•“Answers” the question “What?”
• Example:
• Q: What do you think?
• A: I think Spiderman is the best
Noun Clause (NC) -- continued
• NCs can begin with “that”
• “that” is a subordinating conjunction that
• joins it to an IC
• makes the clause it begins depend on the
IC to complete its meaning.
• “that” is often omitted by native speakers:
• Example:
thinkthat
Spiderman
is the
bestbest
superhero.
I Ithink
Spiderman
is the
superhero.
Adjective Clause (AdjC)
• [S+V/] that acts like an adjective
• Example: The story [that [that
I am reading]
is sad.
I am reading]
S
V
relative
pronoun
This entire clause acts like an adjective,
so it is an adjective clause.
• AdjCs follow nouns
• Often start with relative pronouns
• but the relative pronoun can be omitted
• if the clause has another noun to serve as
the subject
Adverb Clause (AdvC)
• [S+V/] that acts like an adverb
• Example:
[After we drove to the mall] , we looked for a
bookstore.
This clause gives information about how
or why the action happened, so it acts
like an adverb.
• AdvCs always begin with a subordinating conjunction
• after
although
even though
when
if
as
since
because
unless
before
until
Clauses: Building Blocks
for Sentences
A clause is a group of
related words containing
a subject and a verb.
It is different from a phrase in that a phrase does
not include a subject and a verb relationship.
There are many different kinds of clauses. It would be
helpful to review some of the grammar vocabulary we
use to talk about clauses.
Words and phrases in this color are hyperlinks to the Guide to Grammar & Writing.
Clauses: Building Blocks
for Sentences
Clauses go by many names. Here are some definitions:
1. Independent: A clause that can stand by itself and still make
sense. An independent clause could be its own sentence, but is often
part of a larger structure, combined with other independent clauses
and with dependent clauses. Independent clauses are sometimes
called essential or restrictive clauses.
2. Dependent: A clause that cannot stand by itself. It depends on
something else, an independent clause, for its meaning. A
dependent clause trying to stand by itself would be a sentence
fragment. Dependent clauses are sometimes called subordinate,
nonessential, or nonrestrictive clauses. We will review the
different kinds of dependent clauses.
Clauses: Building Blocks
for Sentences
And here are some examples of independent clauses . . . .
1. Independent clauses:
• Glaciers often leave behind holes in the ground.
• These holes are called kettles, and they look just like
scooped-out pots.
• Glaciers also leave behind enormous deposits of glacial
“garbage”; these deposits are called morains.
•Kettle holes result when a large block of ice is left behind
the glacier and then melts away, leaving a large depression.
This last sentence deserves further attention . . . .
Clauses: Building Blocks
for Sentences
Notice that this sentence consists of a very brief independent
clause followed by a long and complex dependent clause.
•Kettle holes result when a large block of ice is left behind
the glacier and then melts away, leaving a large depression.
The dependent clause begins with what is called a
subordinating conjunction. This causes the clause to be
dependent upon the rest of the sentence for its meaning; it
cannot stand by itself.
More on dependent clauses in a moment. . . .
Clauses: Building Blocks
for Sentences
Independent clauses can be connected in a variety of ways:
1. By a comma and little conjunction (and, but, or, nor, for,
yet, and sometimes so).
2. By a semicolon, by itself.
3. By a semicolon accompanied by a conjunctive adverb
(such as however, moreover, nevertheless, as a result,
consequently, etc.).
4. And, of course, independent clauses are often not
connected by punctuation at all but are separated by a period.
Clauses: Building Blocks
for Sentences
Dependent clauses can be identified and classified according to
their role in the sentence.
Noun clauses do anything that a noun can do. They can be
subjects, objects, and objects of prepositions.
• What Turveydrop has forgotten about American politics
could fill entire libraries.
• President Johnson finally revealed what he had in mind for
his congressional leaders.
• Sheila Thistlethwaite has written a marvelous book about
how American politics and economic processes often run
counter to common sense.
Clauses: Building Blocks
for Sentences
Dependent clauses can be identified and classified according to
their role in the sentence.
ADVERB CLAUSES tend to tell us something about the
sentence’s main verb: when, why, under what conditions.
• After Jubal Early invaded the outskirts of Washington,
Congressional leaders took the southern threat more seriously.
• Lincoln insisted on attending the theater that night because it
was important to demonstrate domestic tranquility.
Notice how the dependent clauses begin with “dependent words,”
words that subordinate what follows to the rest of the sentence.
These words are also called subordinating conjunctions.
Clauses: Building Blocks
for Sentences
Dependent clauses can be identified and classified according to
their role in the sentence.
ADJECTIVE CLAUSES modify nouns or pronouns in the
rest of the sentence..
• The Internet, which started out as a means for military and academic
types to share documents, has become a household necessity.
• Tim Berners-Lee, who developed the World Wide Web, could never
have foreseen the popularity of his invention.
•The graphical user interface (GUI) that we all take for granted
nowadays is actually a late development in the World Wide Web.
Notice, now, how the subject is often separated from its verb by
information represented by the dependent clause.
Clauses: Building Blocks
for Sentences
Sometimes an adjective clause has no subject other than the
relative pronoun that introduces the clauses.
The Internet was started in 1969 under a contract let by the
Advanced Research Projects Agency (ARPA) which connected
four major computers at universities in the southwestern US
(UCLA, Stanford Research Institute, UCSB, and the University
of Utah).
Such clauses — all beginning with “which,” “that,” or a form
of “who” — are also known as RELATIVE CLAUSES. The
relative pronoun serves as the subject of the dependent clause
and relates to some word or idea in the independent clause.
Clauses: Building Blocks
for Sentences
Understanding CLAUSES and how they are connected within
the larger structure of your sentence will help you avoid
Sentence Fragments
Run-on Sentences
and make it possible for you to punctuate your sentences
properly and write confidently with a variety of sentence
structures.
Don’t forget to take the
quizzes listed at the end of
the section on clauses.
This PowerPoint presentation was created by
Charles Darling, PhD
Professor of English and Webmaster
Capital Community College
Hartford, Connecticut
copyright November 1999
DISCOVERIES
The Picture by ~1932
q Electrons were discovered ~1900 by
J. J. Thomson
q Protons being confined in a nucleus was
put forth ~1905
q Neutrons discovered 1932 by James Chadwick
q Quantum theory of radiation had
become “widely accepted”, although
even Einstein had his doubts
Quick recap on radiation from atoms
q Energetic gamma rays come from excited nuclei (Co60, for example)
These photons emerge from the nucleus of the atom !!!
q They are generally in the gamma ray region of the EM spectrum
-----------------------------------------------------------------------------q Ordinary atoms also radiate photons when their atomic electrons
“fall” from a higher energy state to a lower one.
(The configuration where all the electrons are in their lowest
energy state is referred to as the ground state)
q The transitions of atomic electrons from a high energy state to a
lower energy state produces radiation (light)!
q The radiation which emerges when electrons make these transitions
(ie., quantum
transitions)
is generally
the visible
X-ray region.
Let’s continue
on this
issue of in
transitions
in or
atoms…
Bohr Atom & Radiation
Before
Electrons circle the nucleus
due to the Electric force
After
Radiated
photon
n=
5
4
3
2
Electron
in lowest
“allowed”
energy level
(n=1)
5
4
3
2
1
Electron
in excited
state
(n=5)
Allowed Orbits
1
Electron falls to
the lowest energy
level
Note: There are many more energy levels beyond n=5, they are omitted for simplicity
Atomic Radiation
It is now “known” that when an electron is in an “excited state”,
it spontaneously decays to a lower-energy stable state.
The difference in energy, ∆E, is given by:
E5 > E4 > E3 > E2 > E1
∆E = E5 – E1 = hν = Εphoton
One example could be:
Energy
E5
Electron
in excited
state
(higher PE)
Energy
Electron
in lowest
state
(lower PE)
n=5
E5
n=5
E4
n=4
E4
n=4
E3
n=3
E3
n=3
E2
n=2
E2
n=2
E1
n=1
E1
n=1
Before
After
h = Planck’s constant = 6.6x10-34 [J s]
ν = frequency of light [hz]
The energy of the light is DIRECTLY
PROPORTIONAL to the frequency, ν.
Recall that the frequency, ν, is related to
the wavelength by:
c=νλ
(ν = c / λ)
So, higher frequency è higher energy
è lower wavelength
This is why UV radiation browns your skin
but visible light does not !
Hydrogen atom energy “levels”
Quantum physics provides the tools to compute the values of
E1, E2, E3, etc…The results are:
2
En = -13.6 / n
5
4
3
2
1
Energy Level
Energy En (eV)
1
-13.6
2
-3.4
3
-1.51
4
-0.85
5
-0.54
These results DO DEPEND ON THE TYPE OF ATOM OR MOLECULE
So, the difference in energy between the 3rd and 1st quantum state is:
Ediff = E3 – E1 = -1.51 – (-13.6) = 12.09 (eV)
When this 3à 1 atomic transition occurs, this energy is released
in the form of electromagnetic energy.
Example 4
In the preceding example, what is the frequency, wavelength of the
emitted photon, and in what part of the EM spectrum is it in?
E = 12.1 [eV]. First convert this to [J].
 1.6x10-19 [J] 
−18
12.1 [eV] 
 = 1.94 x10 [J]
 1 [eV]

Since E = hν è ν = E/h, so:
ν = E/h = 1.94x10-18 [J] / 6.6x10-34 [J s]
= 2.9x1015 [1/s]
= 2.9x1015 [hz]
λ = c/ν = (3x108 [m/s]) / (2.9x1015 [1/s])
= 1.02x10-7 [m]
= 102 [nm]
This corresponds to low energy X-rays !
Some Other Quantum Transitions
Initial
State
2
Final
State
1
Energy diff.
[eV]
10.2
Energy diff. Wavelength Region
[J]
[nm]
1.6x10-18
121
X-ray
3
1
12.1
1.9x10-18
102
X-ray
4
1
12.8
2.0x10-18
97
X-ray
3
2
1.89
3.0x10-19
654
Red
4
2
2.55
4.1x10-19
485
Aqua
5
2
2.86
4.6x10-19
432
Violet
This completed the picture, or did it…
q Electrons were discovered ~1900 by J. J. Thomson
q Protons being confined in a nucleus was put forth ~1905
q Neutrons discovered 1932 by James Chadwick
q Quantum theory of radiation had become
“widely accepted”, although even Einstein
had his doubts
q Radiation is produced when atomic
electrons fall from a state of high
energy à low energy. Yields photons
in the visible/ X-ray region.
q A nucleus can also be excited, and
when it “de-excites” it also gives
Cosmic Rays
q Cosmic Rays are energetic particles that
impinge on our atmosphere (could be from sun
or other faraway places in the Cosmos)
q They come from all directions.
q When these high energy particles strike
atoms/molecules in our atmosphere, they
produce a spray of particles.
q Many “exotic” particles can be created.
As long as they are not so massive as to
violate energy conservation they can be
created.
q Some of these particles are unstable
and “decay” quickly into other stable particles.
q Any of these exotic particles which live long
enough to reach the surface of the earth can be
detected !
Discoveries in Cosmic Rays
Ø 1932 : Discovery of the
antiparticle of the electron,
the positron. Confirmed the
existence and prediction that
anti-matter does exist!!!
Ø 1937 : Discovery of the muon.
It’s very much like a
“heavy electron”.
Ø 1947 : Discovery of the pion.
We’ll touch on these today… and some other things…
Positron Discovery in Cosmic Rays (1932)
Cloud Chamber
Photograph
A “Cloud Chamber” is capable of detecting
charged particles as they pass through it.
The chamber is surrounded by a magnet.
The magnet bends positively charged particles
in one direction, and negatively charged
particles in the other direction.
Lead
plate
Positron
Larger curvature
of particle
above plate
means it’s
moving slower
(lost energy as it
passed through)
By examining the curvature above and below
the lead plate, we can deduce:
(a) the particle is traveling upward in this
photograph.
(b) it’s charge is positive
It’s a particle
who’s mass
is same
Using
other information
about
howasfarelectron
it
but has positive
è it’s
POSITRON
!
traveled,
it can becharge
deduced
not a proton.
Significance of Positron Discovery
The positron discovery was the first evidence for ANTIMATTER.
That is, the positron has
essentially all the same
properties as an electron,
except, it’s charge is
positive !
Carl Anderson
award Nobel
prize for the
discovery of the
positron
Carl Anderson
1905-1991
If an electron and a
positron collide, they ANNIHILATE and
form pure energy (EM Radiation).
This conversion of matter into energy is
a common event in the life of physicists
that studies these little rascals…
Example: Matter à Energy
E=5 [MeV]
E=5 [MeV]
ee++
E=5 [MeV]
e+
e+ %*&*
e+ e- e-
E=5 [MeV]
e- e-
An electron and positron, each
with energy 5 [MeV] collide,
and annihilate into pure energy
in the form of 2 photons.
Each photon carries away ½
of the total energy available.
Example follow-up
In the preceding example, what are the wavelengths of the
photons which emerge from this interaction, and from what
part of the spectrum are they?
Since E=hc / λ, We can get wavelength using: λ = hc/ E
First we need to convert the 5 [MeV] to the equivalent number of [J]
First note that: 5 [MeV] = 5x106 [eV]
-19

1.6x10
[J] 
 = 8.0 x10−13[J]
5x106 [eV]
 1 [eV] 
=1
λ = hc/ E = (6.6x10-34)(3x108) / 8.0x10-13 = 2.5x10-13 [m]
You will find that this corresponds to gamma rays !
Very energetic photons !!!
Discovery of
the muon
q The muon was discovered in 1937 by
J. C. Street and E. C. Stevenson in
a cloud chamber.
q Again, the source is cosmic rays produced
in the atmosphere.
q The muon behaves identally to an electron, except:
It is about 200 times as massive
on these ν guys later !
q It’s unstable, and decays in about 2x10-6 [s]More
= 2 [µs]
q Note that many muons are able to reach the earth from the upper
(µ à
e + νdilation
+ ν) ! Because of their large speed, we
atmosphere because
of time
observe that their “clocks” run slow è they can live longer !!!
Discovery of the Pion
q Cecil Powell and colleagues at Bristol University used
alternate types of detection devices to see charged tracks
(called “emulsions”) in the upper atmosphere.
q In 1947, they annouced the discovery of a particle called
the π-meson or pion (π) for short.
Pion (π)
comes to rest
here, and then
decays:
πàµ+ν+ν
Muon (µ)
comes to rest
here, and then
decays:
µàe+ν+ν
Two neutrinos are also
produces but escape
undetected.
Two more neutrinos
are also produced but
also escape
undetected.
µ
e
π
Cecil Powell
1903-1969
1950 Nobel
Prize winner
The Plethora of Particles
Because one has no control over cosmic rays (energy,
types of particles, location, etc), scientists focused
their efforts on accelerating particles in the lab and smashing them
together. Generically people refer to them as “particle accelerators”.
(We’ll come back to the particle accelerators later…)
Circa 1950, these particle accelerators began to uncover many new
particles.
Most of these particles are
unstable and decay very
quickly, and hence had not
been seen in cosmic rays.
Notice the discovery of the
proton’s antiparticle, the
antiproton, in 1955 !
Energy
What is Energy
From Merriam Webster:
Energy: The capacity for doing work (or to produce heat)
What are some forms/types of energy?
1. Energy of motion (kinetic energy) É
2. Heat
3. Electricity É
4. Electromagnetic waves - like visible light, x-rays, UV rays,
microwaves, etc É
5. Mass É
Huh, what do you mean mass is a form of energy?
We’ll get to this later….
i The thing about energy is that it cannot be created or
destroyed, it can only be transformed from one form into another
Energy Conservation
Like momentum, energy is a conserved quantity.
This provides powerful constraints on what can and cannot happen
in nature.
This is an extremely important concept, and we will come back to
this over and over throughout the remainder of the course.
Kinetic Energy – Energy of Motion
Kinetic energy (KE) refers to the energy associated with the motion
of an object. The kinetic energy is simply:
KE = (½)mv2
where
m = mass in [kg],
v = velocity of object in [m/sec]
and
What are the units of KE?
[KE] = [mass] [velocity]2 = [kg*m2/s2] == [Joule] or just, [J]
A Joule is a substantial amount of energy!
Energy
q The unit, [Joules] applies to all forms of energy, not just KE.
q As we’ll see later, there are sometimes more convenient units
to use for energy.
q You have probably heard of the unit “Watt”. For example,
a 100 Watt light bulb?
A Watt [W] is simply energy usage per unit time, or [J/s].
q So, 100 [W] means the bulb uses 100 [J] per second!
q How many [J] are used by a 100 [W] bulb in 2 minute?
A) 200 [J]
B) 1200 [J]
C) 12000 [J]
D) 2000 [J]
Kinetic Energy Examples
What is the kinetic energy of a 1 [kg] mass moving at 4 [m/sec] ?
1 kg
A) 4 [J]
4 m/sec
B) 0.25 [J]
C) 2 [J]
D) 8 [J]
KE = ½ (1)(4)2 = 8 [J]
What if the mass was going in the opposite direction
(v = - 4 [m/sec])?
1 kg
-4 m/sec
A) 4 [J]
B) 0.25 [J]
C) 2 [J]
D) 8 [J]
KE = ½ (1)(- 4)2= 8 [J]
KE Examples (cont)
q An electron has a mass of 9.1x10-31 [kg]. If it is moving at one-tenth
of the speed of light, what is it’s kinetic energy? The speed of light
is 3x108 [m/sec].
The electron’s velocity is v = (1/10)*(3x108) = 3x107 [m/sec]
So, KE = ½ (9.1x10-31 )(3x107 )2 = 8.2x10-16 [J]
qHow does this compare to the 1 [kg] block moving at 4 [m/sec] ?
KE(electron) / KE(block) = 8.2x10-16/8 = 2.6x10-17 [J]
(Wow, this is a small number. We’ll come back to this fact in a bit…)
Electricity
q Electricity generally refers to the flow of
charges.
q In most cases, electrons are the charges which
are actually moving.
q The units of charge is a Coulomb or simply [C].
q 1 [C] = 6.25x1018 charges (such as electrons or protons)
q Alternately, 1 electron = (1 / 6.25x1018) [C] = 1.6x10-19 [C]
q Charges are made to flow by applying a voltage
q Batteries
q Power Supplies
q Electrical generators
Electrical
Current
q Electrical current is the rate of flow of charges, that is [C/sec]
q The units of current are Amperes, or just Amps == [A]
q 1 [A] = 1 [C/sec]
q 1 [A] = 6.25x1018 charges/sec
q Lightening bolts can contain several thousand amps of current !
Electrical Energy and the Electron-Volt
q How much energy does an electron gain as it is accelerated
across a voltage? (Length of arrow is proportional to velocity)
-1000 [V]
e
e
e
e
e
e
+1000 [V]
q It’s energy is the product of the charge times the voltage. That is,
E = q(∆V)
= (1.6x10-19)(2000)
= 3.2x10-16 [J]
Charge: q is in [C]
Voltage: ∆V is in [Volts] ([V])
Energy: E is in [Joules] ([J]).
q Because 1 electron is only a tiny fraction of a Coulomb, the energy
is also tiny ! This is a pain, but ….
The Electron-Volt (eV)
qHow much energy does an electron gain as it crosses 1 volt.
Energy = q*(∆V) = (1.6x10-19 [C]) * (1 [Volt]) = 1.6x10-19 [J]
q Since this amount of energy is so small, we define a more
convenient unit of evergy, called the “Electron-Volt”
Define the electron-Volt:
1 [eV] = 1.6x10-19 [J]
q An electron-volt is defined as the amount of energy an electron
would gain as it accelerates across 1 Volt.
q In most cases, we will use the [eV] as our unit of energy. To
convert back to [J], you need only multiply by 1.6x10-19.
Examples
An electron is accelerated across a gap which has a voltage of 5000 [V]
across it. How much kinetic energy does it have after crossing the gap?
E = (1 electron)(5000 V) = 5000 [eV]
A proton is accelerated across a gap which has a voltage of 10,000 [V]
across it. How much kinetic energy does it have after crossing the gap?
E = (1 proton)(10000 V) = 10,000 [eV]
(we don’t refer to them as “proton-volts” !)
Electromagnetic Waves
• Electromagnetic (EM) waves are
another form of energy.
• In the “classical” picture, they are
just transverse waves...
The speed of EM waves
in “vacuum” is always
c = 3 x 108 [m/sec]
The wavelength (λ) is the
distance from crest-to-crest
In vacuum
c = 3x108 [m/sec] for
all wavelengths !
(~3x108 [m/sec] in air too)
The Electromagnetic Spectrum (EM)
Shortest wavelengths
(Most energetic)
Recall
109 [nm] = 1 [m]
106 [µm] = 1 [m]
Longest wavelengths
(Least energetic)
Frequency
Consider two waves moving to the right at the
speed c, and count the number of waves which
pass a line per second
1, 2, 3, 4,
5, 6, 7, 8,
9, 10 …
14 waves
7 waves
q Since all EM waves move at the same speed, they would measure
twice as many waves for the top wave as the bottom wave.
q We call the number of waves that pass a given point per second the
frequency
Frequency (cont)
q The frequency is usually symbolized by the greek letter, ν (“nu”)
ν == frequency
q Frequency has units of [number/sec], or just [1/sec],
or [hertz] == [hz]
q A MegaHertz [Mhz] is 1 million hertz, or 1 million waves/second!
q There is a simple relation between the speed of light, c, the
wavelength, λ, and the frequency ν.
c = λν
c = 3x108 [m/sec]
Example I
What is the frequency of a gamma-ray with λ=10-6 [nm] ?
I want to use c = λν, but we need λ in [m]…
So, first convert [nm] to [meters]
10-6 [nm] * (
1 [m])
( 109 [nm] )
= 10-15 [m]
ν = c / λ = (3x108) / (1x10-15)
= 3 x 1023 [hz]
= 300,000,000,000,000,000,000,000 waves/sec !
That’s A LOT of waves!
Example II
What is the frequency of a gamma-ray with λ=0.5 [km] ?
First, convert [km] to [m]…
0.5 [km] * ( 103 [ m ] )
(
1
[km] )
= 5x102 [m]
ν = c / λ = (3x108) / (5x102)
= 6 x 105 [hz]
= 0.6 [Mhz]
This is AM Radio!
this is the case…
FM Radio waves are typically around 80 Mhz. Show that
Mass Energy
According to Einstein’s Theory of Special Relativity,
Mass is a form of Energy,
and they are related by the simple and well-known formula:
E=
2
mc
The units of energy, E can be expressed in [J], as before, but it is
more convenient to use the electron-volt [eV].
Recall that 1 [eV] = 1.6x10-19 [J]
E=mc2
q The important point here is that energy and mass are really
equivalent, and are related to one another by simply the speed of
light (c) squared!
q This equation implies that even if a particle is at rest, it in fact
does have a “rest-mass energy” given by this formula.
Example I
q What is the rest-mass energy of a 1 [kg] block in [J].
E = mc2 = (1 [kg])(3x108 [m/sec])2 = 9x1016 [J] .
This is a HUGE amount of energy stored in the rest mass!
q Really, how much energy is this?
To put it in context, you could power a 100 [Watt] light bulb for 29
million years if you could convert all of this rest mass to energy !!!!
Unfortunately, this is not possible at this point…
Example II
q What would be the kinetic energy of this 1 [kg] block if it were
moving at 200 [m/sec] (about 430 [mi/hr]) ?
KE = ½ (1 [kg]) (200 [m/sec])2 = 2x104 [J]
q What fraction of the rest mass energy is this ?
Fraction = (2x104 [J] ) / (9x1016 [J] ) = 2.2x10-13
( or 0.000000000022%)
è That is, the KE is only a tiny fraction of the rest mass energy.
Alternately, it gives you a flavor for how much energy is
bottled up in the rest mass !!!
Example III
qWhat is the rest mass energy of a neutron, which has a mass
of 1.68x10-27 [kg]? Express the result in [eV].
E = mc2 = (1.68x10-27 [kg])(3x108 [m/sec])2 = 1.5x10-10 [J]
q Now convert to [eV].
1.5x10-10 [J] * (
1 [ eV ] )
= 9.4x108 [eV]
( 1.6x10-19 [J] )
= 940 [MeV]
Example IV
An electron and positron (a positively-charged electron) each having
10 [keV] collide and annihilate into pure energy. How much energy
is carried away after the collision?
Total energy is conserved, so it must be the same as
before the collision.
10 keV + 10 keV = 20 keV
Summary
q There are many forms of energy, including:
Energy of motion
Electrical energy
Electromagnetic energy (EM waves)
Mass energy
q Energy of motion is given by KE=(1/2)mv2
q One of the most important forms of energy which we’ll deal with
is mass energy.
q Mass IS a form of energy.
q Mass can be converted into energy. If you convert all of the
mass of some object with mass M to energy, the corresponding
energy will be E=Mc2.
LIGHT – PHOTONS
The Wave – Particle Duality
OR
Light Waves
Until about 1900, the classical wave theory of light described
most observed phenomenon.
Light waves:
Characterized by:
Ø Amplitude (A)
Ø Frequency (ν)
Ø Wavelength (λ)
Energy α A2
And then there was a problem…
However, in the early 20th century, several effects were
observed which could not be understood using the wave theory
of light.
Two of the more influential observations were:
1) The Photo-Electric Effect
2) The Compton Effect
I will describe each of these today…
Photoelectric Effect (I)
“Classical” Method
What if we try this ?
Increase energy by
increasing amplitude
Vary wavelength, fixed amplitude
electrons
emitted ?
No
No
No
No
electrons
emitted ?
No
Yes, with
low KE
Yes, with
high KE
No electrons were emitted until the frequency of the light exceeded
a critical frequency, at which point electrons were emitted from
the surface!
(Recall: small λ è large ν)
Photoelectric Effect (II)
q Electrons are attracted to the (positively charged) nucleus by the
electrical force
q In metals, the outermost electrons are not tightly bound, and can
be easily “liberated” from the shackles of its atom.
q It just takes sufficient energy…
Classically, we increase the energy
of an EM wave by increasing the
intensity (e.g. brightness)
Energy α A2
But this doesn’t work ??
PhotoElectric Effect (III)
q An alternate view is that light is acting like a particle
q The light particle must have sufficient energy to “free” the
electron from the atom.
q Increasing the Amplitude is just simply increasing the number
of light particles, but its NOT increasing the energy of each one!
è Increasing the Amplitude does diddly-squat!
q However, if the energy of these “light particle” is related to their
frequency, this would explain why higher frequency light can
knock the electrons out of their atoms, but low frequency light
cannot…
Photo-Electric Effect (IV)
q In this “quantum-mechanical” picture, the energy of the
light particle (photon) must overcome the binding energy of the
electron to the nucleus.
q If the energy of the photon does exceed the binding energy, the
electron is emitted with a KE = Ephoton – Ebinding.
q The energy of the photon is given by E=hν, where the
constant h = 6.6x10-34 [J s] is Planck’s constant.
“Light particle”
Before Collision
After Collision
Photons
q Quantum
theory describes light as
a particle called a photon
q According
to quantum theory, a photon has an energy given by
E = hν = hc/λ
h = 6.6x10-34 [J*sec]
Planck’s constant, after the scientist Max Planck.
q The
energy of the light is proportional to the frequency, and inversely
proportional to the wavelength! The higher the frequency (lower
wavelength) the higher the energy of the photon!
q 10
photons have an energy equal to ten times a single photon.
q The
quantum theory describes experiments to astonishing
precision, whereas the classical wave description cannot.
The Electromagnetic Spectrum
Shortest wavelengths
(Most energetic photons)
E = hν = hc/λ
h = 6.6x10-34 [J*sec]
(Planck’s constant)
Longest wavelengths
(Least energetic photons)
Interpretation of Photoelectric Effect
Vary wavelength, fixed amplitude
electrons
emitted ?
Increase
Energy
Increase
Energy
E1 = hν1
No
E2 = hν2
Yes, with
low KE
E3 = hν3
Yes, with
high KE
E3 > E2 > E1
Photoelectric Effect Applet
The Compton Effect
In 1924, A. H. Compton performed an experiment
where X-rays impinged on matter, and he measured
the scattered radiation.
Incident X-ray
wavelength
λ1
M
A
T
T
E
R
Scattered X-ray
wavelength
λ2
Louis de Broglie
λ2 > λ1
e
Electron comes flying out
Problem: According to the wave picture of light, the incident X-ray
gives up energy to the electron, and emerges with a lower energy
(ie., the amplitude is lower), but must have λ2=λ1.
Quantum Picture to the Rescue
q If we treat the X-ray as a particle with zero mass, and momentum
p = E / c, everything works !
Incident X-ray
p1 = h / λ1
Electron
initially at
rest
Scattered X-ray
p2 = h / λ2
λ2 > λ1
e
e
pe
Compton found that if the photon was treated like a particle
with mometum p=E/c, he could fully account for the energy &
momentum (direction also) of the scattered electron and photon!
Just as if 2 billiard balls colliding!
Interpretation of Compton Effect
“Light particle”
λ1
λ2
Before Collision
After Collision
The Compton Effect describes collisions of light with electrons
perfectly if we treat light as a particle with:
p = h/λ
and
E = hν
= hc/λ = (h/λ)c
= pc
DeBroglie’s Relation
p=h/λ
è The smaller the wavelength the larger the photon’s momentum!
è The energy of a photon is simply related to the momentum by:
E = pc
(or,
p=E/c )
è The wavelength is related to the momentum by: λ = h/p
è The photon has momentum, and its momentum is given
by simply p = h / λ .
Momentum of Photons
If I have a photon with energy E=1 [GeV], what is its momentum?
p = E / c = (1 [GeV])/c = 1 [GeV/c] … That’s it!
If I have a photon with momentum 5 GeV/c, what is its energy?
E = pc = (5 GeV/c) * c = 5 [GeV] … whallah !
So, the only difference between a photons’ energy and momentum is:
Energy
è [GeV]
momentum è [GeV/c]
Don’t forget though that the “c” in [GeV/c] really means 3x108 [m/s].
Scattering Problem
Incident X-ray
wavelength
Electron
initially at
rest
λf
λi=1.5 [nm]
e
e
KE=0.2 [keV]
Before
After
q Compute the energy of the 1.5 [nm] X-ray photon.
E = hc/λ = (6.6x10-34 [J s])(3x108 [m/s]) / (1.5x10-9 [m])
= 1.3x10-16 [J]
Scattering Example (cont)
q Express this energy in [keV].
1.3x10-16 [J] * (1 [eV] / 1.6 x10-19 [J]) = 825 [eV] = 0.825 [keV]
q What is the magnitude of the momentum of this photon?
p = E / c = 0.825 [keV]/ c = 0.825 [keV/c]
q After the collision the electron’s energy was found to be 0.2 [keV].
What is the energy of the scattered photon?
A) 0.2 [keV]
B) 0.625 [keV]
C) 1.025 [keV]
D) 0.825 [keV]
Since energy must be conserved, the photon must have E=0.825-0.2 = 0.625 [keV]
q What would be the wavelength of the scattered photon?
HW exercise !
Summary of Photons
q Photons can be thought of as
“packets of light” which behave as a
particle.
q To describe interactions of light with matter, one generally has to
appeal to the particle (quantum) description of light.
q A single photon has an energy given by
E = hc/λ,
where
h = Planck’s constant = 6.6x10-34 [J s]
c = speed of light
= 3x108 [m/s]
λ = wavelength of the light (in [m])
and,
q Photons also carry momentum. The momentum is related to the
energy by:
p = E / c = h/λ
Matter Waves ?
One might ask:
“If light waves can behave like a particle, might particles act like waves”?
The short answer is YES. The explanation lies in the realm of
quantum mechanics, and is beyond the scope of this course.
However, you already have been introduced to the answer.
Particles also have a wavelength given by:
λ = h/p = h / mv
è That is, the wavelength of a particle depends on its momentum,
just like a photon!
è The main difference is that matter particles have mass, and
photons don’t !
Matter Waves (cont)
Compute the wavelength of a 1 [kg] block moving at 1000 [m/s].
λ = h/mv = 6.6x10-34 [J s]/(1 [kg])(1000 [m/s]) = 6.6x10-37 [m].
è This is immeasureably small. So, on a large scale, we cannot
observe the wave behavior of matter
Compute the wavelength of an electron (m=9.1x10-31 [kg])
moving at 1x107 [m/s].
λ = h/mv = 6.6x10-34 [J s]/(9.1x10-31 [kg])(1x107 [m/s])
= 7.3x10-11 [m].
This is near the wavelength of X-rays
Electron Microscope
èThe electron microscope is a device which uses the
wave behavior of electrons to make images
which are otherwise too small using visible light!
This image was taken with a Scanning
Electron Microscope (SEM).
These devices can resolve features down
to about 1 [nm]. This is about 100 times
better than can be done with visible light
microscopes!
IMPORTANT POINT HERE:
High energy particles can be used to reveal the structure of matter !
Remarks on Particle Probes
q We have now asserted that high energy particles (electrons in the
case of a SEM) can provide a way to reveal the structure of matter
beyond what can be seen using an optical microscope.
q The higher the momentum of the particle, the smaller the
deBroglie wavelength.
q As the wavelength decreases, finer and finer details about the
structure of matter are revealed !
q We will return to this very important point.
è To explore matter at its smallest size, we need very high
momentum particles!
è Today, this is accomplished at facilities often referred to as
“atom-smashers”. We prefer to call them “accelerators”
è More on this later !
What is Matter
If you took a piece of paper, and ripped it
in half.
Take one of the halves, and rip it in half.
Repeat this again & again & again…
At what point would you find that you couldn’t
subdivide the material anymore?
What would you have in your hand at this point?
A very good reference for the things we are going to cover is at:
http://particleadventure.org/particleadventure/frameless/sitemap.html
What is matter ?
Ü We are ! And lots of other things
around us…
Almost everything around you is
matter…
But, what we’re really interested
in is:
What is matter at its most
fundamental level ?
What are we made of ?
q We’re made of cells which
contain DNA.
- Different cells serve different
functions in your body.
q The cells contain a nucleus,
which contains your DNA !
q And the DNA is a wonderful,
complex chain of molecules
which contains your genetic
code!
q But, what are molecules
made of ?
0.0002”
The Elements
†Molecules are complex structures of the elements
But what’s inside “an element”
For each element, we can associate an atom.
Prior to ~1905, nobody really knew:
“ What does the inside of an atom look like ? ”
Early
“Plum-Pudding”
Model
Positive
Charge
(uniformly
distributed)
Corpuscles
(Electrons)
The positive charge is spread
out like a “plum-pudding”
A digression on radiation
Radiation: The process of emitting
energy in the form of waves or
particles.
Where does radiation come from?
Radiation is generally produced
when particles interact or decay.
A large contribution of the radiation
on earth is from the sun (solar) or
from radioactive isotopes of the
elements (terrestrial).
Radiation is going through you at
this very moment!
http://www.atral.com/U238.html
Isotopes
What’s an isotope?
Two or more varieties of an element
having the same number of protons but
different number of neutrons. Certain
isotopes are “unstable” and decay to
lighter isotopes or elements.
Deuterium and tritium are isotopes of
hydrogen. In addition to the 1 proton,
they have 1 and 2 additional neutrons in
the nucleus respectively*.
Another prime example is
Uranium-238, or just 238U.
Radioactivity
By ~1900, it was known that certain isotopes emit
penetrating rays. Three types of radiation were known:
1) Alpha particles (α)
2) Beta particles
(β)
3) Gamma-rays
(γ)
Where do these ‘particles’ come
from ?
qThese particles generally come
from the nuclei of atomic isotopes
which are not stable.
q The decay chain of Uranium
produces all three of these forms
of radiation.
q Let’s look at them in more detail…
Note: This is the
atomic weight, which
is the number of
protons plus neutrons
Alpha Particles (α)
Radium
Radon
R226
Rn222
88 protons
138 neutrons
86 protons
136 neutrons
+
n p
p n
α (4He)
2 protons
2 neutrons
The alpha-particle (α) is a Helium nucleus (charge = +2)
It’s the same as the element Helium, but without the
electrons !
Beta Particles (β)
Carbon
C14
Nitrogen
N14
6 protons
8 neutrons
7 protons
7 neutrons
n
à
+
e-
+
ν
electron
(beta-particle)
p + e- + ν
More on this
bugger later…
The electron emerges with relatively high energy in this
“disintegration” (decay) process.
We see that one of the neutrons from the C14 nucleus
“converted” into a proton, and an electron was ejected.
The remaining nucleus contains 7p and 7n, which is a nitrogen
nucleus. In symbolic notation, the following process occurred:
Gamma particles (γ)
In much the same way that electrons in atoms can be in an
excited state, so can a nucleus.
Neon
Ne20
10 protons
10 neutrons
(in excited state)
Neon
Ne20
+
10 protons
10 neutrons
(lowest energy state)
gamma
A gamma is a high energy light particle (short for gamma ray).
It is NOT visible to your naked eye because it is not in
the visible part of the EM spectrum.
Gamma Rays
Neon
Ne20
Neon
Ne20
+
The gamma from nuclear decay
is in the X-ray/ Gamma ray
part of the EM spectrum
(very energetic!)
How do these particles differ ?
Particle
Mass
Charge
Gamma (γ)
0
0
Beta (β)
(Electron)
Alpha (α)
Electron mass is
~1/2000th of
a proton’s mass
~4 times a proton’s
mass (since mp≈ mn).
Back to “Structure of Matter”
-1
+2
mp = proton mass
mn = neutron mass
Scattering Experiments
If the plum-pudding model was right, then matter
is “soft”. There’s no “central, hard core”…
Alpha
particle
source
Ernest Rutherford
1871-1937
Awarded the
Nobel Prize in 1908
Calculations, based on the known laws of electricity and magnetism
showed that the heavy alpha particles should be only slightly deflected
by this “plum-pudding” atom…
Au Contraire
Contrary to expectations, Rutherford found that a significantly
large fraction (~1/8000) of the alpha particles “bounced back” in
the same direction in which they came…The theoretical expectation
was that fewer than 1/10,000,000,000 should do this ???
Gold foil
α
Huh ???
α
In Rutherford’s words…
“It was quite the most incredible event that ever happened to me in
my life. It was as if you fired a 15-inch naval shell at a piece of tissue
paper and the shell came right back and hit you.”
The (only) interpretation
The atom must have a solid core capable of imparting large
electric forces onto an incoming (charged) particle.
α
α
α
α
α
The Modern Atom
Atom: the smallest particle of an element that can exist either
alone or in combination
Electrons
Nucleus
2x10-13 cm
0.0000000002 cm
(2 x 10-10 cm)
Atoms and Space
Approximately what fraction of the volume of an atom does the
nucleus consume?
Assume that an atom can be approximated by a sphere with a
radius given by the electrons orbit radius?
Use the following data.
• The radius of the nucleus is ~ 2x10-13 cm.
• The electrons orbits at a radius of ~ 2x10-10 cm
• Ignore the electrons size, as it is unimportant.
• The volume of a sphere is (4/3)πR3.
Answer…
a) First find the volume of the entire atom
Volume = (4/3)*π∗(2x10-10)3 = 3.4 x 10-29 cm3
b) Now find the volume which contains the nucleus.
Volume = (4/3)*π∗(2x10-13)3 = 3.4 x 10-38 cm3
c) Now compute the fraction:
Fraction = (3.4 x 10-38 / 3.4 x 10-29 ) = 0.000000001
In other words, 99.99999999% of an atom is empty space !!!
Matter & Forces
Matter
Hadrons
Baryons
Mesons
Quarks
Anti
Anti-Quarks
Quarks
Leptons
Charged Neutrinos
Forces
Gravity
Weak
Strong
EM
A Sense of Scale
~5x10-6
[m]
Quarks and leptons
are the most elementary
particles we know about
at this time. They are no
larger than 10-18 [cm]
~2x10-9
[m]
~2x10-8
[m]
~5x10-15
[m]
~1.5x10-15
[m]
<1x10-18
[m]
q
e
The Standard Model
q Quarks and leptons are the most
fundamental particles of nature
that we know about.
q Up & down quarks and electrons
are the constituents of ordinary matter.
q The other quarks and leptons can
be produced in cosmic ray showers
or in high energy particle accelerators.
q Each particle has a corresponding
antiparticle.
The cast of quarks & leptons
Family
Quarks
Antiquarks
Q = +2/3
Q = -1/3
Q = -2/3
Q = +1/3
1
u
d
u
d
2
c
s
c
s
3
t
b
t
b
Family
1
Leptons
Q = -1
Q=0
eνe
Antileptons
Q = +1
Q=0
e+
νe
2
µ−
νµ
µ+
νµ
3
τ−
ντ
τ+
ντ
Quarks versus Leptons
What are the primary differences between quarks and leptons?
Ultimately, what differentiates the quarks & leptons from one
another are the forces which each may exhibit.
We therefore now embark on the concept of forces.
The Four Fundamental Forces
Weaker
1. Gravity
2. Weak Force
Stronger
3. Electromagnetic force
4. Strong Force
Doesn’t that look
like George W. ?
All other forces you know about can be attributed to one of these!
Gravity
Gravity is the weakest of the 4 forces. The gravitational force
between two objects of masses m1 and m2, separated by a distance
d is:
F = Gm1m2/d2
G = gravitational constant = 6.7x10-11[N*m2/kg2]
d = distance from center-to-center
The units of each are:
[Force] = [Newton] = [N]
[mass] = [kg]
[distance] = [meters]
Gravity is only an attractive force
The Electric Force
In the old days, we believed that “force” was transmitted more or
less instantaneously by a “field of force”.
Lines of force
p
p
p
p
p
The proton to the right is repelled by the “electric field” created by
the one on the left (electrical repulsion).
The New Concept of Force
In the 1960’s, a new theory of interactions
was developed.
At the heart of it is the concept that:
Richard Feynman, 1918-1988
1965 Nobel Prize in Physics
Forces are the result of the exchange of
“force carriers” between the two particles
involved in the interaction.
The force carrier of the electromagnetic force is the
photon (γ)
The Photon (γ)
Property
Mass
Charge
Value
0
0
q The photon is the “mediator” of the
electromagnetic interaction
q The photon can only interact with objects which
have electric charge !!!!!
!Note that all particles involved
(other than the photon)
carry electrical charge!
Electron-Positron Scattering
e+ + e-
à
e+ + e-
e+
e+
e+
e+
e-
e-
ee-
Electron-Positron Scattering
e+ + e-
à
e+ + e-
e+
e+
e+
e-
ee-e-
Electron-Positron Annihilation
e+ + e-
à
e+
e+
e+
e+ee-
γ
γ
e+ + e-
ee-
Electron-Positron Annihilation
e+ + e-
à
e+
e+
e+
e+ee-
γ
γ
e+ + e-
ee-
Quark Pair Production
à
e+ + e-
q + q
e+
e+
e+
e+ee-
γ
γ
ee* Note: Two completely different particles in the “final state”. Since
quarks have electric charge, this can in fact happen!
Quark Pair Production
à
e+ + e-
q + q
e+
e+
e+
e+ee-
γ
ee* Note: Two completely different particles in the “final state”
In the preceding example, assume that the incoming electron and
positron each have energy of 5 GeV.
Example
1. What is the energy of the photon after the electron & positron annihilate?
A) 5 GeV
B) 10 GeV
C) 0 GeV
D) None of these
2. Assuming that the final state electron & positron have equal energy,
what is the energy of the emergent electron ?
A) 5 GeV
B) 10 GeV
C) 0 GeV
D) None of these
3.
Once the photon is produced, it may split into any particle-antiparticle pair
which is permissible by energy conservation. For each of these, tell whether
the photon can produce the final state particles:
a) u and u (Mu~0.005 GeV)
Y or N
b) d and d (Md ~ 0.010 GeV)
Y or N
c) s and s (MS ~ 0.20 GeV)
Y or N
d) c and c (MC ~ 1.5 GeV)
Y or N
e) b and b (Mb ~ 4.8 GeV)
Y or N
f) t and t (Mt ~ 175 GeV)
Y or N
Photon Conversion
γ
γ
γ
γ
à
γ
γ
e+ + e-
Photon Conversion
γ
γ
γ
γ
à
γ
γ
e+ + e-
Quark Antiquark Annihilation
q + q
à
e+ + e-
q
q
q
qeq
γ
γ
q
q
* Note: Reverse process to quark pair production!
Quark Antiquark Annihilation
à
q + q
e+ + e -
q
q
q
qeq
γ
q
q
* Note: Reverse process to quark pair production!
Feynman Diagrams
q A great simplification which allows us to
represent these physical processes are facilitated
by Feynman Diagrams.
qIt turns out, they can also be used to calculate
the probability for the process to occur
(Beyond the scope of this module though).
q We will use them more in a qualitative sense
to visualize various processes.
Feynman Diagrams
e+
e-
Electron-Positron
Annihilation
γ
e-
e+
e+
Electron-Positron
Scattering
e+
γ
e-
etime
Photon Conversion and Emission
ePhoton Conversion
γ
e+
γ
Photon Emission
e-
e-
More Feynman Diagrams
Quark Pair
Production
§“q” can be any quark,
as long as there is
enough energy to create
2 of ‘em!
Quark Antiquark
Annihilation to
Electron & Positron
e+
e-
q
γ
q
q
q
e+
γ
e-
The paragraph is a series of sentences
developing
one topic.
The Topic Sentence
• The topic of a paragraph is
stated in one sentence. This is
called the topic sentence.
The rest of the paragraph consists
of sentences that develop or
explain the main idea.
•
Through the centuries rats
have managed to survive all our
efforts to destroy them. We have
poisoned them and trapped
them. We have fumigated,
flooded, and burned them. We
have tried germ warfare. Some
rats even survived atomic bomb
tests conducted on Entwetok
atoll in the Pacific after World
War II. In spite of all our
efforts, these enemies of ours
continue to prove that they are
the most indestructible of pests.
Developing a Paragraph
Unity in the Paragraph
Every sentence in a paragraph should support the main
idea expressed in the topic sentence.
The concluding or
clincher sentence
• Restate the topic sentence in different words.
• A clincher sentence or concluding sentence
clinches the point made in the paragraph.
• It summarizes the paragraph.
Coherence in a Paragraph
• Stick to the point: The ideas have
a clear and logical relation to each other.
• Put details or examples or
incidents in logical order.
chronological
in relation to each other
in order of importance
4
3
2
1
Connecting Sentences
Within the Paragraph
Transition words
chronological
order
objects in relation to in order of
importance
one another
first
next to
however
meanwhile
in front of
furthermore
later
beside
as a result
afterwards
between
in fact
finally
behind
yet
Types of Paragraphs
• The narrative paragraph
• tells a story
• The persuasive paragraph.
• tries to convince the audience
• The descriptive paragraph
• describes something
• The expository or explanatory paragraph
• gives information or explains something
Welcome to Particle Physics
A blurb from the “Quarks Unbound” from the
American Physical Society
•
“We’re barely aware that they are there, but the elementary particles of matter
explain much of what we take for granted every day. Because of gluons
binding the atomic nucleus, matter is stable and doesn’t crumble. Because of
gravitons, our feet stay firmly planted on the ground. We see because our
eyes react to photons of light. “
•
“Particle Physics explains the ordinary, and delights us with tales of the
extraordinary. Antimatter annihilates matter. “Virtual” particles blink in and
out of existence in the vacuum of space. Neutrinos zip through the Earth
untouched.”
•
“Particle Physics doesn’t stop at the unusual either. It contemplates the
cosmic too, exploring the origins of the universe and the symmetries that
frame its design.”
Aims of Particle Physics
1. To understand nature at it’s most fundamental level.
2. What are the smallest pieces of matter, and how do
they make up the large scale structures that we see
today ?
3. How and why do these ‘fundamental particles’
interact the way that they do?
4. Understand the fundamental forces in nature.
In this course, our aim is to
introduce you to nature at its
most fundamental level
q Some of the concepts you will encounter may not agree with
your intuition, others will…
q We strongly encourage you to ask questions in class.
It will help you, your classmates, and us!
Before we can get to this, we will first spend some time on
some basics, and then we’ll get to the meat later on….
Sizes and Powers of 10
q In describing nature, objects vary dramatically in size.
q The solar system is about 10,000,000,000,000,000,000,000 times
larger than an atom, for example è Scientific notation !
q You should become comfortable with seeing scientific notation,
in the context of relative sizes of objects.
q Useful Web Sites which allow you to step through the powers of
10 are at:
q http://cern.web.cern.ch/CERN/Microcosm/P10/english/P0.html
q http://www.wordwizz.com/pwrsof10.htm
q http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/
Powers of 10
10 = 101
Positive
Powers
100 = 10 x10 = 101 x101 = 102
1000 = 10 x10 x10 = 10 x10 x10 = 10
1
1
1
3
1
1
0.1 =
= 1 = 10−1
10 10
Negative
Powers
0 Power
1
1 1
1
0.01 =
= x = 2 = 10−2
100 10 10 10
1
1 1 1
1
0.001 =
= x x = 3 = 10−3
1000 10 10 10 10
100 = 1
Scientific Notation
12500 = 1.25 x 10000 = 1.25 x (10 x 10 x 10 x 10) = 1.25 x 104
1.25x10?
1.2500
12500.0
Move decimal 4 places to right
0.00367 = 3.67 x 0.001 = 3.67 x (.1 x .1 x .1) = 3.67 x 10-3
3.67x10?
0.00367
3.67
Move decimal 3 places to left
The earth has a circumference of about 25,000 miles. How is this
expressed in scientific notation?
A) 2.5x103
B) 25x104
C) 2.5x104
D) None of these
The sun has a radius of 695 million meters. How is this expressed
in scientific notation?
A) 695x105
B) 6.95x108 C) 6.95x109 D) 6.95x106
Multiplying powers of 10
The circumference of the earth is about 4x107 [m]. If I were to
travel around the earth 3x102 times, how many [m] will I have gone?
A) 7.0x109
B) 1.2x1010
C) 1.0x1015
D) 7.0x1015
(4x107) x (3x102) = (4x3) x (107x102) = 12x10(7+2) = 12x109
= (1.2x10) x109
= 1.2x1010
A bullet takes 10-3 seconds to go 1 [m]. How many seconds will it
take for it to go 30 [m]?
A) 3.0x10-1
B) 3.0x10-2
C) 4.0x10-2
D) 4.0x10-1
(1x10-3) x (3x101) = (1x3) x (10-3x101) = 3x10(-3+1) = 3x10-2
Dividing Powers of 10
A gas truck contains 4.6x103 gallons of fuel which is to be distributed
equally among 2.0x104 cars. How many gallons of fuel does each car
get?
A) 2.3x101
B) 2.3x10-1
C) 23
D) 2.3
3
3
4.6 x10
4.6 10
(3− 4)
−1
=
* 4 = 2.3 x10
= 2.3 x10
4
2.0 x10
2.0 10
The area of the U.S is about 3.6x106 [miles], and the population is
about 300x106. On average, what is the population density in persons
per square mile?
A) 1.2x102
B) 1.2x10-1
C)1.2x10-3
D)1.2x10-2
6
6
3.6 x10
3.6 10
(6 −8)
−2
=
* 8 = 1.2 x10
= 1.2 x10
8
3.0 x10
3.0 10
Common Prefixes
Commonly used prefixes
indicating powers of 10
103 = “kilo”
106 = “mega”
109 = “giga”
1012 = “tera”
10-3 = “milli”
10-6 = “micro”
10-9 = “nano”
10-12 = “pico”
10-15 = “femto”
How many times larger is a kilometer than a micrometer ?
A) 1,000
B) 1,000,000
C) 1,000,000,000
D) 1x10-9
è1 km = 103 m and there are 106 micrometers in a meter, so
there are 109 (or 1 billion) micrometers in 1 km
How many 100 W bulbs can be kept lit with 100 Tera-Watts?
A) 1.0x107
B) 1.0x109
C) 1.0x1012
D)1.0x1013
Common Conversions
Length:
Mass:
Speed:
2.54 [cm] = 1 [inch]
1 [kg] = 2.2 [lbs]
1 [m/sec] = 2.25 [mi/hr]
How many meters are there in a centimeter?
A) 100
B) 0.01
C) 1000
D) 0.001
How many inches in 1 kg ?
A) 2.54
B) 25.4
C) less than 25
D) None of these
Units
q Joe asks Rob… “About how much does your car weigh” ?
Joe answers … “About 1.5”
q Is Joe’s answer correct or incorrect?
Physical quantities have units !!!!!!!!
qAll physical quantities have units, and they must be used.
q One exception is if you are talking only about a pure number.
For example: How many seats are in this classroom?
q I will often use brackets to indicate units:
1 kilogram == 1 [kg]
Variables/Symbols
q It is often more convenient to represent a number using a letter.
For example, the speed of light is 3x108 [m/sec]. To avoid having to
write this every time, we simply use the letter c which represents
this value. That is c = 3x108 [m/sec].
q We might use the expression, “the particle is moving at 0.1c”.
This should be interpreted as
“The particle is moving at 1/10th of the speed of light.”
q We will often use letters to represent constants or variables, so
you must become comfortable with this.
Proportionality
What do we mean when we say:
“Quantity A is proportional to quantity B”
This means the following:
1) If we double B, then A also doubles.
2) If we triple B, then A also triples.
3) If we halve B, then A also halves.
This is often written as: A α B
The circumference of a circle, C, is proportional to the radius, R.
If the radius is increased by a factor of 10, what happens to the
circumference?
It increases by a factor of 10
Proportionality Exercises
q Consider this 1 cm square
l
q What is its area?
Area = base * height = l*l = l2 = (1 cm )2 = 1 cm2
q What’s the area of this square?
2l
l
l
Area = base * height = 2l*2l = 4l2 = 4(1 cm )2 = 4 cm2
If we double the length of the side,
we quadruple the area?
Proportionality Exercises (cont)
The area of a circle is proportional to the radius squared.
What happens to the area of a circle if the radius is doubled?
Radius = 2 cm
Radius = 4 cm
A=πr2
A=π(22) = 4π
A=π(42) = 16π
Since A α r2, (A=πr2)
doubling the radius quadruples the area !
Inverse Proportionality
What do we mean when we say a quantity V is
inversely proportional to another quantity, say d.
V α (1/d)
It means:
If we double d, then V is reduced by a factor of 2
If we quadruple d, then V is reduced by a factor of 4.
Why?
We know that Vd α (1/d)
If we double d, then d à (2*d), so
V2d α [1/(2d)] = (1/2) (1/d) = (1/2) Vd.
In the same way, show that V4d = (1/4) Vd
Exercises
The force of gravity is known to be inversely proportional to
the square of the separation between two objects. What happens to the
force between two objects when the distance is tripled?
A)
B)
C)
D)
Increases by a factor of 6
Decreases by a a factor of 8
Decreases by a factor of 9 
Decreases by a factor of 6
The electric force between two charges is also known to be inversely
proportional to the square of the separation. What happens to the force
if the distance is reduced by a factor of 10.
A)
B)
C)
D)
Increases by a factor of 10
Increases by a a factor of 100 
Decreases by a factor of 10
Decreases by a factor of 100
Algebra
If a car is going 20 [mi/hr] for 4 [hrs], how far does the car go?
A) 80 [mi]
B) 5 [mi]
C) 20 [mi]
D) none of these
What did you do to arrive at this result?
q You multiplied the speed (20 [mi/hr]) by the time (4 [hrs]).
q So, to get the distance, you did this:
distance = velocity * time
d = v*t
Algebra (cont)
If a biker goes 20 [mi] in 2 [hrs], what is the bikers average speed ?
A) 20 [mi/hr]
B) 5 [mi/hr]
C) 10 [mi/hr] D) 40 [mi/hr]
What did you do to arrive at this result?
q You divided the distance (20 [mi]) by the time (2 [hrs]).
q That is, you reasoned:
average velocity = distance / time
v=d/t
Is this equation and the previous one expressing
different relationships among the variables v, d and t?
Algebra (cont)
NO!
d=v*t
and
v=d/t
Are expressing the
same relationship. The
variables are just
shuffled around a bit!
Ø To cast the first form into the second:
Multiply both sides by (1/t):
The factor of t * (1/t) = 1, so
And, (1/t)*d = d/t,
Or, just switching sides…
d=v*t
(1/t)* d = v * t *(1/t)
(1/t)* d = v
d/t=v
v=d/t
An important example
Einstein’s famous Energy-mass relation:
E = m c2
Can be rearranged to read:
m = E / c2
Note that the units of mass can also be expressed in units of
Energy / (speed)2
(We’ll come back to this point later…)
Summary
For this module, you should be comfortable with:
1. Using and manipulating powers of 10 (division, multiplication).
2. Understanding what “proportional to” and “inversely
proportional to” mean.
3. Simple conversion of units, if you are given the conversion
factors. (e.g. [in.] to [cm], [cm] to [m]., etc)
4. Basic algebra and manipulating equations such as, E=mc2,
c=fλ , E=hf , etc.
5. Understanding prefixes, such as Giga, Tera, Mega, etc.
English Grammar
Parts of Speech
Eight Parts of Speech
Nouns
Interjections
Adjectives
Conjunctions
Word that names
• A Person
bA
Place
b A Thing
b An Idea
Kinds of Nouns
Common Nouns
Proper Nouns
John
Mary
Singular Nouns
Plural Nouns
boys
girls
Plural Possessive
boys’
girls’
boy
girl
boy
girl
Singular Possessive
boy’s
girl’s
A word that expresses action or
otherwise helps to make a
statement
“be” verbs
&
taste
feel
sound
look
appear
become
seem
grow
remain
stay
Every sentence must have
a
Kinds of Verbs
• Action verbs express
mental or physical
action.
He rode the horse to
victory.
• Linking verbs make a
statement by
connecting the subject
with a word that
describes or explains
it.
He has been sick.
The pronoun is a word used in place of one or more nouns.
It may stand for a person, place, thing, or idea.
Indefinite Pronouns
anybody
each
either
none
someone, one, etc.
Modifies or describes a
noun or pronoun.
Did you lose your address
book?
Is that a wool sweater?
Just give me five minutes.
Answers these questions:
Modifies or describes
a verb, an adjective,
or another adverb.
Answers the questions:
He ran quickly.
She left yesterday.
We went there.
It was too hot!
To what degree or how much
Interrogative
Adverbs
introduce questions
How did you break your
leg?
How often do
you run?
Where did you put the
mouse trap?
A preposition introduces a noun or pronoun
or a phrase or clause functioning in the sentence
as a noun. The word or word group that the
preposition introduces is its object.
They received a postcard from Bobby telling
about his trip to Canada.
The preposition
never stands alone!
object of
preposition
preposition
object
You can press those leaves under glass.
can have more than
one object
Her telegram to Nina and Ralph brought good news.
object can have modifiers
It happened during the last examination.
Some Common Prepositions
aboard
about
above
across
after
against
along
among
around
at
before
behind
below
beneath
beside
between
beyond
by
down
during
except
for
from
in
into
like
of
off
on
over
past
since
through
throughout
to
toward
under
underneath
until
up
upon
with
within
without
The conjunction
a word that joins words
or groups of words.
A conjunction is
or
but
The interjection
is an exclamatory word that expresses
emotion
Goodness! What a cute baby!
Wow! Look at that
sunset!
That’s all for now. . .
More Later
Introduction to Physical
Quantities
Scalars
Scalar quantities are those which are described solely by their
magnitude
Some examples are:
Mass
Time
Volume
Temperature
Voltage
e.g.
e.g.
e.g.
e.g
e.g.
14 [kg], 36 [lbs], …
10 seconds, 40 minutes, …
1000 cm3, 4 litres, 12 gallons
14 oF , 25 oC, …
9 Volts, etc
Vectors
Vector quantities are those which need to be described by BOTH
magnitude and direction
Some of the most common examples which we will encounter are:
Velocity
e.g. 100 [mi/hr] NORTH
Acceleration
e.g. 10 [m/sec2] at 35o with respect to EAST
Force
e.g. 980 [Newtons] straight down (270o)
Momentum
e.g. 200 [kg m/sec] at 90o.
Distance
q The separation between two locations.
q Distance can be measured in many types of units. We will mostly use:
MKS Units
millimeters [m]
centimeters [cm]
meters [m]
kilometers [km],
etc
FYI : 1 [km] = 0.6 [mi]
qYou should be comfortable with converting from [cm] to [m],
[mm] to [km], and so on.
q We may use the symbolic notation ∆d to mean a change in the
position.
The symbol ∆ should be read as “the change in”
Time
In physics, we are most often less interested in absolute time than
changes in time, or a time interval.
seconds [sec]
minutes [min]
hours [hr]
Time can be expressed in several units as well:
days
years
etc…
Example 1: How much time does it take for the earth to make one
revolution?
Example 2: How long did it take for you to drive to the store today?
We usually refer to a time interval as : ∆t
Velocity
Velocity is a measure of the rate of change of the distance with
respect to time.
v = ∆d / ∆t
q It will usually be measured in [m/sec].
q What does 5 [m/sec] mean?
q It means if an object passes by us at 5 [m/sec], it will advance its
position by 5 [m] every second. So after 2 [sec], it will have
advanced 10 [m], and 20 [m] in 4 [sec] and so on.
If a train moves at 50 [meters/sec], how far will it go in 50 seconds ?
a) 100 miles
b) 2.5 [km]
c) 250 [m]
d) 2500 miles
Acceleration (I)
qAcceleration is the rate of change of velocity with respect to time
a = ∆v / ∆t
[a] = [m/sec] / [sec] = [m/sec2]
q What does a = 5 [m/sec2] mean?
If an object starts at rest, its velocity increases by 5 [m/sec]
every second.
Time (sec)
0
1
2
3
4
Acceleration
5 m/sec2
5 m/sec2
5 m/sec2
5 m/sec2
5 m/sec2
Velocity
0 m/sec
5 m/sec
10 m/sec
15 m/sec
20 m/sec
Acceleration (II)
Acceleration can be negative also! We call this deceleration.
q If the acceleration is in the same direction as the velocity,
the object has positive acceleration (it speeds up).
q If the acceleration is in the opposite direction as the velocity,
the object has negative acceleration or deceleration (it slows down).
Deceleration: Animated GIF of car decelerating
What is a Force ?
Force is simply:
A PUSH
or
A PULL
Forces have both magnitude
and direction
Force and Acceleration
q Experimentally, we find that if we apply a force
to an object, it accelerates.
q We also find that the acceleration (a) is directly
proportional to the applied force (F) and inversely
proportional to the mass (m) . That is:
Isaac Newton
a=F/m
This means:
Ø Increasing the force increases the acceleration;
decreasing the force results in a lower acceleration.
This is Newton’s Law, and it is often written:
F = ma
Force (I)
q A force is generally a result of an interaction between two (or more)
objects (Try and think of a scenario where a force is applied with only
one object involved)?
q Can you think of some examples of forces?
ü Gravitational
ü Electric
ü Magnetic
ü Friction
ü Wind drag
ü Van der Waals forces
ü Hydrogen bonds
ü Forces in a compressed or stretched spring
+…
Forces (II)
q Since two or more objects must be involved, a force intimately
tied to the notion of an interaction.
q Interactions are now believed to occur through the exchange of
“force carriers”. This is a very important point, and we’ll come
back to it later…
q So far, we know only of four types of fundamental forces in
nature:
q Gravity, Electromagnetic, Weak, and Strong
q We will come back to each of these
q All other forces in nature are understood to be the residual effects
of these fundamental forces
Momentum (I)
What is momentum?
Momentum is simply the product of the mass and the velocity.
Denoting momentum as p, it is simply:
m
v
p = m*v
q The units of momentum are [kg][m/sec] == [kg m/sec]
q Momentum is a very important subject in physics because it is
what we call a conserved quantity. What does this mean?
q We will come back to the idea of conserved quantities in physics.
They play a very important role in understanding the world around us!
Momentum (Example I)
If a 500 [kg] car is traveling west at 20 [m/sec], what is
its momentum?
A) -1x104 [kg m/sec]
B) -1x103 [kg m/sec]
C) 25 [kg m/sec]
D) 1x105 [kg m/sec]
-20 [m/sec]
500 [kg]
p = mv
= (500 [kg])(-20 [m/sec])
= -10,000 [kg m/sec]
= -1x104 [kg m/sec]
Momentum (Example II)
If a 5000 [kg] truck is travelling east at 10 [m/sec], what is its
momentum?
A) -5x104 [kg m/sec]
B) 5x104 [kg m/sec]
C) 500 [kg m/sec]
D) 1x104 [kg m/sec]
5000 [kg]
p = m*v
= (5000 [kg])(10 [m/sec])
= 50,000 [kg m/sec]
= 5x104 [kg m/sec]
10 [m/sec]
Momentum (Example III)
If the car and the truck collide, what is the total momentum of the
car and truck just before impact?
A) 6x104 [kg m/sec]
B) -4x104 [kg m/sec]
C) 4x104 [kg m/sec]
D) 0 [kg m/sec]
10 [m/sec]
5000 [kg]
-20 [m/sec]
500 [kg]
Since their momenta are aligned in the same direction, we can
just add them:
PTOTAL = -1x104 [kg m/sec] + 5x104 [kg m/sec] = 4x104 [kg m/sec]
Energy
Energy: The capacity for doing work (or to produce heat)
What are some forms/types of energy?
1. Energy
of motion (kinetic energy) É
2. Heat
3. Electricity É
4. Electromagnetic waves - like visible light, x-rays, UV rays,
microwaves, etc É
5. Mass É
Energy
What do you mean mass is a form of energy?
We’ll get to this later….
i The thing about energy is that it cannot be created or
destroyed, it can only be transformed from one form into
another
i Yes, like momentum it is a “conserved” quantity. We will
learn that conserved quantities are a powerful tool in
“predicting the future”!
Summary I
q In nature, there are two types of quantities, scalars and vectors
q Scalars have only magnitude, whereas vectors have both
magnitude and direction.
q The vectors we learned about are distance, velocity, acceleration,
force, and momentum
q The scalars we learned about are time, and Energy.
Summary II
q Forces are the result of interactions between two or more
objects.
q If the net force on an object is not zero, it will accelerate. That
is it will either speed up, slow down, or change direction.
q Energy and momentum are conserved quantities. This has
far-reaching consequences for predicting whether certain “events”
or “processes” can occur.
q There are many forms of energy. The topic of energy will
be discussed in greater detail in next lecture.
The Modern Quantum Atom
The nucleus and the discovery
of the neutron
What are electron-volts ?
The Quantum atom
Rutherford’s Picture of the Atom
Electrons circle the nucleus
due to the Coulomb force
Corpuscles
(Electrons)
~10-14 m
~10-11 m
Positively
Charged
Nucleus
This model was inspired by the results of scattering alpha-particles
off of heavy nuclei (like gold, silver, etc).
James Chadwick and the Neutron
Circa 1925-1935
Picked up where Rutherford left off with more
scattering experiments… (higher energy though!)
q Performed a series of scattering experiments
with α-particles (recall a particles are He nucleus),
4
2 He
+ 9 Be
12
C+
1
0
n
q Chadwick postulated that the emergent radiation
was from a new, neutral particle, the neutron.
q Applying energy and momentum conservation
he found that the mass of this new object
was ~1.15 times that of the proton mass.
Awarded the Nobel Prize in 1935
1891-1974
***Electron-Volts (eV)***
q When talking about subatomic particles, and individual photons,
energies are very small (~10-12 or smaller).
q It’s cumbersome to always deal with these powers of 10.
q We introduce a new unit of energy, called the electron-volt (eV).
q An [eV] is equivalent to the amount of energy a single electron gains
when it is accelerated across a voltage of 1 [V].
Electric
TV tube accelerates electrons
GPE using 20,000 [V] = 20 [kV].
1 kg
Potential
10[J]
0 [V]
+
1m
0 [kV]
0 [J]
-
-20 [kV]
q Your
-20 [kV]
More on [eV]
How much energy does an electron gain when it is accelerated across
a voltage of 20,000 [V] ?
E = 20,000 [eV]
[V]
is a unit of “Potential”
[eV] is a unit of Energy (can be converted to [J])
How can you convert [eV] to [J] ?
Not too hard… the conversion is: 1 [eV] = 1.6x10-19 [J]
So, let’s do an example !
Convert 20 [keV] to [J].
Since the “k” == kilo = 1000 = 103, 20 [keV] = 20,000 [eV] = 2x104 [eV]
-19

1.6x10
[J] 
4
−15
2x10 [eV] 
 = 3.2 x10 [J]
 1 [eV]

=1
It’s a lot easier to say “20 [keV]” than 3.2x10-15 [J] !
Even more on [eV]
So, [eV] IS A UNIT OF ENERGY;
It’s not a “type” of energy (such as light, mass, heat, etc).
When talking about energies of single photons, or of subatomic particles,
we often use this unit of energy, or some variant of it.
So,
1 [eV] = 1.6x10-19 [J] (can be used to go back & forth between
these two energy units)
1 [keV] = 1000 [eV] = 103 [eV]
1 [MeV] = 1,000,000 [eV] = 106 [eV]
1 [GeV] = 1,000,000,000 [eV] = 109 [eV]
“k = kilo (103)””
“M = mega (106)”
“G = giga (109)”
Example 1
A Cobalt-60 nucleus is unstable, and undergoes a decay where a 1173 [keV] photon is
emitted. From what region of the electromagnetic spectrum does this come?
The energy is 1173 [keV], which is
1173 [keV] = 1173x103 [eV] = 1.173x106 [eV].
* First convert this energy to [J],
E = 1.173x106 [eV] * (1.6x10-19 [J] / 1 [eV])
= 1.88x10-13 [J]
* Now, to get the wavelength, we use:
E = hc/λ, that is λ = hc/E.
So, λ = 6.63x10-34[J s]*3x108[m/s]/1.88x10-13 [J]
= 1.1 x 10-12 [m]
* Now, convert [m] to [nm],
1.1 x 10-12 [m] * (109 [nm] / 1 [m])
= 1.1x10-3 [nm]
è It’s a GAMMA Ray
Example 2
An electron has a mass of 9.1x10-31 [kg].
What is it’s rest mass energy in [J] and in [eV].
E = mc2 = 9.1x10-31*(3x108)2 = 8.2x10-14 [J]
Now convert to [eV]
 1 [eV] 
5
=
8.2x10 [J] 
5.1x10
[eV]=0.51 [MeV]

-19
 1.6x10 [J] 
-14
What is an electron’s rest mass?
According to Einstein, m = E/c2, that is:
[mass] = [Energy] / c2
m = E / c2 = 0.51 [MeV/c2]
Example 3
A proton has a mass of 1.67x10-27 [kg].
What is it’s rest mass energy in [J] and in [eV].
E = mc2 = 1.67x10-27 *(3x108)2 = 1.5x10-10 [J]
Now convert to [eV]
 1 [eV] 
8
=
1.5x10 [J] 
9.4x10
[eV]=940 [MeV]

-19
 1.6x10 [J] 
-10
What is a proton’s rest mass?
According to Einstein, m = E/c2, that is:
[mass] = [Energy] / c2
m = E / c2 = 940 [MeV/c2]
Proton vs Electron Mass
How much more massive is a proton than an electron ?
Ratio = proton mass / electron mass
= 940 (MeV/c2) / 0.51 (MeV/c2) = 1843 times more massive
You’d get exactly the same answer if you used:
electron mass = 9.1x10-31 [kg]
Proton mass = 1.67x10-27 [kg]
Using [MeV/c2] as units of energy is easier…
Neils Bohr and the Quantum Atom
Circa 1910-1925
q Pointed out serious problems with
Rutherford’s atom
Ø Electrons should radiate as they orbit the
nucleus, and in doing so, lose energy, until
they spiral into the nucleus.
ØAtoms only emit quantized amounts of
energy (i.e., as observed in Hydrogen spectra)
q He postulated
Ø Electric force keeps electrons in orbit
Ø Only certain orbits are stable, and they do
not radiate energy
Radiation is emitted when an e- jumps from
an outer orbit to an inner orbit and the energy
difference is given off as a radiation.
1885-1962
Awarded the Nobel Prize in 1922
Bohr’s Picture of the Atom
Before
Electrons circle the nucleus
due to the Electric force
After
Radiated
photon
n=
5
4
3
2
Electron
in lowest
“allowed”
energy level
(n=1)
5
4
3
2
1
Electron
in excited
state
(n=5)
Allowed Orbits
1
Electron falls to
the lowest energy
level
Note: There are many more energy levels beyond n=5, they are omitted for simplicity
Atomic Radiation
It is now “known” that when an electron is in an “excited state”,
it spontaneously decays to a lower-energy stable state.
The difference in energy, ∆E, is given by:
E5 > E4 > E3 > E2 > E1
∆E = E5 – E1 = hν = Εphoton
One example could be:
Energy
E5
Electron
in excited
state
(higher PE)
Energy
Electron
in lowest
state
(lower PE)
n=5
E5
n=5
E4
n=4
E4
n=4
E3
n=3
E3
n=3
E2
n=2
E2
n=2
E1
n=1
E1
n=1
Before
After
h = Planck’s constant = 6.6x10-34 [J s]
ν = frequency of light [hz]
The energy of the light is DIRECTLY
PROPORTIONAL to the frequency, ν.
Recall that the frequency, ν, is related to
the wavelength by:
c=νλ
(ν = c / λ)
So, higher frequency è higher energy
è lower wavelength
This is why UV radiation browns your skin
but visible light does not !
Hydrogen atom energy “levels”
Quantum physics provides the tools to compute the values of
E1, E2, E3, etc…The results are:
2
En = -13.6 / n
5
4
3
2
1
Energy Level
Energy En (eV)
1
-13.6
2
-3.4
3
-1.51
4
-0.85
5
-0.54
These results DO DEPEND ON THE TYPE OF ATOM OR MOLECULE
So, the difference in energy between the 3rd and 1st quantum state is:
Ediff = E3 – E1 = -1.51 – (-13.6) = 12.09 (eV)
When this 3à 1 atomic transition occurs, this energy is released
in the form of electromagnetic energy.
Example 4
In the preceding example, what is the frequency, wavelength of the
emitted photon, and in what part of the EM spectrum is it in?
E = 12.1 [eV]. First convert this to [J].
 1.6x10-19 [J] 
−18
12.1 [eV] 
 = 1.94 x10 [J]
 1 [eV]

Since E = hν è ν = E/h, so:
ν = E/h = 1.94x10-18 [J] / 6.6x10-34 [J s]
= 2.9x1015 [1/s]
= 2.9x1015 [hz]
λ = c/ν = (3x108 [m/s]) / (2.9x1015 [1/s])
= 1.02x10-7 [m]
= 102 [nm]
This corresponds to low energy X-rays !
Some Other Quantum Transitions
Initial State
Final State
Energy diff. Energy diff. Wavelength
[eV]
[J]
[nm]
10.2
1.6x10-18
121
2
1
3
1
12.1
1.9x10-18
102
4
1
12.8
2.0x10-18
97
3
2
1.89
3.0x10-19
654
4
2
2.55
4.1x10-19
485
5
2
2.86
4.6x10-19
432
4
3
0.66
1.05x10-19
1875
This completed the picture, or did it…
q Electrons were discovered ~1900 by J. J. Thomson
q Protons being confined in a nucleus was put forth ~1905
q Neutrons discovered 1932 by James Chadwick
q Quantum theory of radiation had become
“widely accepted”, although even Einstein
had his doubts
q Radiation is produced when atomic
electrons fall from a state of high
energy à low energy. Yields photons
in the visible/ X-ray region.
q A nucleus can also be excited, and
when it “de-excites” it also gives
QUARKS
What IS Matter ?
• Matter is all the “stuff” around you!
• Here’s the picture we’re going to uncover
(not all today though)
Matter
Hadrons
Baryons
Mesons
Quarks
Anti
Anti-Quarks
Quarks
Leptons
Charged Neutrinos
Forces
Gravity
Weak
Strong
EM
We’re going to work our way
from the largest size objects
which we know about to the
smallest size objects which we
know about
Where does all this come from?
The universe is a very big place!
It is filled with galaxies much like
our own, the Milky Way
There are likely ~100 billion of them
which we can “see”.
Each of these galaxies contain around
100 billion stars.
Fig: Small section of the universe, from
the Hubble Space Telescope (HST)
Our Milky Way galaxy is simply one of them.
Our Sun is just one of the 10,000,000,000,000,000,000,000 stars
in the universe!
Our Galaxy: The Milky Way
How big is the Milky Way (M.W.)?
Its radius is about 100,000 light years !
How far is a light year (l.y.)?
It’s the distance light travels in
1 year!
So, 1 l.y. = 5,870,000,000,000 miles
(5.9x1012 mi.) !
So, the M.W. Galaxy radius is about
600,000,000,000,000,000 (6x1017) miles
in radius!
Us
(Our Solar
System)
The Center of our Solar System:
The Sun
At the center of our solar system is
our star, the Sun
It’s diameter is ~100 times that of
the earth, which implies you could
fit ~1,000,000 earths inside the sun!
It’s is ~330,000 times as massive
as the Earth
The Sun (cont)
It is a thermonuclear reactor. Inside
the sun, hydrogen is being converted
into helium.
In this process, energy is released in
the form of heat, electromagnetic waves
(UV, visible light), neutrinos, etc.
It’s surface temperature is
~10,000 OC; other parts of the
sun can be as hot as 15,000,000 OC.
So, it’s HOT !
Our Solar System: The Planets
3.6 billion miles
Earth is at about 94 million miles
from the Sun
The Planets
q The figure shows relative sizes of the planets
q Distances between planets not drawn to scale
q Astronomically, we’re pretty tiny!
3.6 billion miles
Pluto
Earth
Saturn
(Diam ~ 25000 mi.)
Sun
Jupiter
Uranus
Neptune
The Earth
Mass : 6 x 1024 [kg]
Radius: 6.4 million meters
Africa
Ahhh, and finally we’re back home
q So, to set the scale:
q From here to California
2,500 miles
q From here to the next closest
star
25,000,000,000,000 miles
(25 trillion miles)
q Like traveling back and forth to
California 10 billion times
Not very practical to get even to the next closest star!
Exercise
The next closest star is about
25 trillion miles away. How long
would it take an spacecraft moving
at 20,000 miles/hr to get to this star?
Well, every hour the spacecraft goes 20,000 miles (2x104 miles)
So, the time it would take would be:
(25 x 1012 [miles]) / 2x104 [miles/hr] = 1.25 billion hours
= 52 million days
= 143,000 years
= 1,430 centuries!
And then there’s US !
Ü We’re very small compared to
the vast universe!
ÜHowever, there are things
which are a lot smaller than us.
What are we made of ?
q We’re made of cells which
contain DNA.
- Different cells serve different
functions in your body.
q Cells contain a nucleus,
which holds your DNA !
q And the DNA is simply a
complex chain of molecules
which contains your genetic
code!
q And what are molecules
made of ?
0.0002”
The Elements
†Molecules are complex structures of the elements
The Atom
Electrons
Nucleus
5x10-15 m
0.0000000002 m
(2 x 10-10 m)
Atoms and Space
Approximately what fraction of the volume of an atom does the
nucleus consume?
Assume that the nucleus and the atom can be approximated via
spheres with the radii given below?
Use the following data.
• The radius of the nucleus is ~ 5x10-15 [m].
• The electrons orbits at a radius of ~ 2x10-10 [m]
• Ignore the electrons size, as it is unimportant.
• The volume of a sphere is (4/3)πR3.
Answer…
a) First find the volume of the entire atom
Volume = (4/3)*π∗(2x10-10)3 = 3.4 x 10-29 [m3]
b) Now find the volume which contains the nucleus.
Volume = (4/3)*π∗(5x10-15)3 = 5.2 x 10-43 [m3]
c) Now compute the fraction:
Fraction = (5.2 x 10-43 / 3.4 x 10-29 ) = 0.000000000000015
In other words, more than 99.99999999% of an atom is empty space !!!
What’s in the Nucleus?
Protons
Protons are
positively charged
and that amount
of charge is exactly
equal (and opposite)
to the charge of the
electron
Neutrons
Neutrons are
similar to protons
(ie., similar mass), but
have a net charge of
zero.
Recall: 1 [fm] = 10-15 [m]
Are protons and neutrons
fundamental?
(By fundamental, I mean are they indivisible?
The answer is NO !
Protons and neutrons are made of smaller objects called quarks!
1x 10-18 m
(at most)
ØProtons
2 “up” quarks
1 “down” quark
(1.6 x 10-15 m)
ØNeutrons
1 “up” quark
2 “down” quarks
Three Families of Quarks
Generations
Increasing mass
Woohhh,
fractionally
charged
particles?
Charge =
-1/3
Charge =
+2/3
I
II
III
d
s
b
(down)
(strange)
(bottom)
u
c
t
(up)
(charm)
(top)
Also, each quark has a corresponding antiquark.
The antiquarks have opposite charge to the quarks
The 6 Quarks, when & where…
Quark
Date
Where
Mass
[GeV/c2]
Comment
up,
down
-
-
~0.005,
~0.010
Constituents of hadrons,
most prominently, proton and
neutrons.
strange
1947
-
~0.2
discovered in cosmic rays
~1.5
Discovered simultaneously in
both pp and e+e- collisions.
~4.5
Discovered in collisions of
protons on nuclei
~175
Discovered in pp collisions
charm
1974
bottom
1977
top
1995
SLAC/
BNL
Fermilab
Fermilab
How do we know
any of this?
qRecall that high energy particles
provide a way to probe, or
“see” matter at the very smallest
sizes. (Recall Electron microscope
example).
q Today, high energy
accelerators produce energetic
beams which allow us to probe
matter at its most fundamental level.
q As we go to higher energy particle collisions:
1) Wavelength probe is smaller è see finer detail
2) Can produce more massive objects, via E=mc2
Major High Energy Physics Labs
Fermilab
DESY
SLAC
CERN
CESR
BNL
KEK
Fermilab Accelerator
(30 miles from Chicago)
Experimental areas
Tevatron
Top Quark
discovered
here at FNAL
in 1995.
1.25 miles
Main Injector
“Typical” Particle Detector
Typical physicist colleagues!
Don’t ask me what they’re doing !
Summary
q Protons and neutrons are made of up & down quarks.
q The strange quark was uncovered in cosmic rays via their “strange”
behavior.
q Today, accelerators produce high energy beams of particles
which illuminate the structure of matter.
* Smaller deBroglie wavelength è finer microscope
* Can produce massive particles which haven’t been around
since the Big Bang! (E=mc2)
q The charm, bottom and top quarks were all discovered by producing
them artificially at high energy accelerators.
Radioactivity
Radiation
Radiation: The process of emitting
energy in the form of waves or
particles.
Where does radiation come from?
Radiation is generally produced
when particles interact or decay.
A large contribution of the radiation
on earth is from the sun (solar) or
from radioactive isotopes of the
elements (terrestrial).
Radiation is going through you at
this very moment!
Isotopes
What’s an isotope?
Two or more varieties of an element
having the same number of protons but
different number of neutrons. Certain
isotopes are “unstable” and decay to
lighter isotopes or elements.
Deuterium and tritium are isotopes of
hydrogen. In addition to the 1 proton,
they have 1 and 2 additional neutrons in
the nucleus respectively*.
Another prime example is Uranium
238, or just 238U.
Radioactivity
By the end of the 1800s, it was known that certain
isotopes emit penetrating rays. Three types of radiation
were known:
1) Alpha particles (α)
2) Beta particles
(β)
3) Gamma-rays
(γ)
Where do these particles come
from ?
qThese particles generally come
from the nuclei of atomic isotopes
which are not stable.
q The decay chain of Uranium
produces all three of these forms
of radiation.
q Let’s look at them in more detail…
Note: This is the
atomic weight, which
is the number of
protons plus neutrons
Alpha Particles (α)
Radium
Radon
R226
Rn222
88 protons
138 neutrons
+
86 protons
136 neutrons
n p
p n
α (4He)
2 protons
2 neutrons
The alpha-particle (α) is a Helium nucleus.
It’s the same as the element Helium, with the
electrons stripped off !
Beta Particles (β)
Carbon
C14
Nitrogen
N14
6 protons
8 neutrons
7 protons
7 neutrons
+
eelectron
(beta-particle)
We see that one of the neutrons from the C14 nucleus
“converted” into a proton, and an electron was ejected.
The remaining nucleus contains 7p and 7n, which is a nitrogen
nucleus. In symbolic notation, the following process occurred:
nàp+e (+ν)
Yes, the same
neutrino we saw
previously
Gamma particles (γ)
In much the same way that electrons in atoms can be in an
excited state, so can a nucleus.
Neon
Ne20
10 protons
10 neutrons
(in excited state)
Neon
Ne20
+
10 protons
10 neutrons
(lowest energy state)
gamma
A gamma is a high energy light particle.
It is NOT visible by your naked eye because it is not in
the visible part of the EM spectrum.
Gamma Rays
Neon
Ne20
Neon
Ne20
+
The gamma from nuclear decay
is in the X-ray/ Gamma ray
part of the EM spectrum
(very energetic!)
How do these particles differ ?
Particle
Mass*
(MeV/c2)
Charge
Gamma (γ)
0
0
Beta (β)
~0.5
-1
Alpha (α)
~3752
+2
* m = E / c2
Rate of Decay
qBeyond knowing the types of particles which are emitted
when an isotope decays, we also are interested in how frequently
one of the atoms emits this radiation.
q A very important point here is that we cannot predict when a
particular entity will decay.
q We do know though, that if we had a large sample of a radioactive
substance, some number will decay after a given amount of time.
q Some radioactive substances have a very high “rate of decay”,
while others have a very low decay rate.
q To differentiate different radioactive substances, we look to
quantify this idea of “decay rate”
Half-Life
The “half-life” (h) is the time it takes for half the atoms of a
radioactive substance to decay.
For example, suppose we had 20,000 atoms of a radioactive
substance. If the half-life is 1 hour, how many atoms of that
substance would be left after:
#atoms
remaining
% of atoms
remaining
1 hour (one lifetime) ?
10,000
(50%)
2 hours (two lifetimes) ?
5,000
(25%)
3 hours (three lifetimes) ?
2,500
(12.5%)
Time
Lifetime (τ)
The “lifetime” of a particle is an alternate definition of
the rate of decay, one which we prefer.
It is just another way of expressing how fast the substance
decays..
It is simply: 1.44 x h, and one often associates the
letter “τ” to it.
The lifetime of a “free” neutron is 14.7 minutes
{τ (neutron)=14.7 min.}
Let’s use this a bit to become comfortable with it…
Lifetime (I)
Ø The lifetime of a free neutron is 14.7 minutes.
Ø If I had 1000 free neutrons in a box, after 14.7
minutes some number of them will have decayed.
Ø The number remaining after some time is given by the
radioactive decay law
N = N 0e
−t /τ
N0 = starting number of
particles
τ = particle’s lifetime
This is the “exponential”. It’s
value is 2.718, and is a very useful
number. Can you find it on your
calculator?
Lifetime (II)
N = N0e
Note by slight rearrangement of this formula:
Fraction of particles which did not decay:
−t /τ
N / N0 = e-t/τ
1.20
0τ
1τ
2τ
3τ
4τ
5τ
0
14.7
29.4
44.1
58.8
73.5
Fraction of
remaining
neutrons
1.0
0.368
0.135
0.050
0.018
0.007
1.00
Fraction Survived
#
Time
lifetimes (min)
0.80
0.60
0.40
0.20
0.00
0
2
4
6
8
10
Lifetimes
After 4-5 lifetimes, almost all of the
unstable particles have decayed away!
Lifetime (III)
q Not all particles have the same lifetime.
q Uranium-238 has a lifetime of about 6 billion
(6x109) years !
q Some subatomic particles have lifetimes that are
less than 1x10-12 sec !
q Given a batch of unstable particles, we cannot
say which one will decay.
q The process of decay is statistical. That is, we can
only talk about either,
1) the lifetime of a radioactive substance*, or
2) the “probability” that a given particle will decay.
Lifetime (IV)
q Given a batch of 1 species of particles, some will decay
within 1 lifetime (1τ), some within 2τ, some within 3τ, and
so on…
q We CANNOT say “Particle 44 will decay at t =22 min”.
You just can’t !
q All we can say is that:
q After 1 lifetime, there will be (37%) remaining
q After 2 lifetimes, there will be (14%) remaining
q After 3 lifetimes, there will be (5%) remaining
q After 4 lifetimes, there will be (2%) remaining, etc
Lifetime (V)
q If the particle’s lifetime is very short, the particles
decay away very quickly.
q When we get to subatomic particles, the lifetimes
are typically only a small fraction of a second!
q If the lifetime is long (like 238U) it will hang around
for a very long time!
Lifetime (IV)
What if we only have 1 particle before us? What can we say
about it?
Survival Probability = N / N0 = e-t/τ
Decay Probability = 1.0 – (Survival Probability)
# lifetimes Survival Probability
(percent)
1
2
3
4
5
37%
14%
5%
2%
0.7%
Decay Probability =
1.0 – Survival Probability
(Percent)
63%
86%
95%
98%
99.3%
Summary
q Certain particles are radioactive and undergo decay.
q Radiation in nuclear decay consists of α, β, and γ particles
q The rate of decay is give by the radioactive decay law:
Survival Probability = (N/N0)e-t/τ
q After 5 lifetimes more than 99% of the initial particles
have decayed away.
q Some elements have lifetimes ~billions of years.
q Subatomic particles usually have lifetimes which are
fractions of a second… We’ll come back to this!
The Need for a “Strong Force”
Why do protons stay together in the nucleus, despite
the fact that they have the same electric charge?
è They should repel since they are like charge
Why do protons and neutrons in the nucleus bind
together?
è Since the neutron is electrically neutral, there should
be no EM binding between protons and neutrons.
Search for a Theory of Strong
Interactions
q By the 1960’s, Feynman et al, had fully developed a “quantum”
theory which accounted for all EM phenomenon. This theory is
called Quantum Electrodynamics (or QED for short).
q Because of this remarkable success, scientists developed an
analogous theory to describe the strong interaction. It is called
Quantum Chromodynamics (or QCD for short).
q Scientists conjectured that, like the EM force, there is also a
quantum of the strong force, and called it the gluon.
The Strong Force
q For the EM interactions, we learned that:
The photon mediates the interaction between objects
which carry electrical charge
q For the Strong Interactions, we conjecture that:
A force carrier, called the gluon mediates the interaction
between objects which carry color charge (that is, the
quarks, and …gluons !).
q The most striking difference between the gluon and the
photon is:
The gluon carries color charge, but the photon does not
carry electric charge.
è Gluons can interact with other gluons !!!!
Comparison
Strong and EM force
Property
EM
Strong
Force Carrier
Photon (γ)
Gluon (g)
Mass
0
0
Charge ?
None
Yes, color charge
Charge types
+, -
red, green, blue
Couples to:
All objects with
electrical charge
Range
Infinite (1/d2)
All objects with
color charge
ˆ10-14 [m]
(inside hadrons)
Color Charge of Quarks
q Recall, we stated, without much explanation, that quarks come in
3 colors.
q “color charge”
çè
“electrical charge” çè
strong-force
EM force.
as
q Experiments show that there are 3 colors; not 2, not 4, but 3.
q Again, this does not mean that if you could see quarks, you
would see them as being colored. This “color” that we refer to is
an “intrinsic property” and color is just a nice way to visualize it.
Color of Hadrons (II)
BARYONS
q1
q2
RED + BLUE + GREEN = “WHITE”
or “COLORLESS”
q3
MESONS
q
q
q
q
q
q
GREEN + ANTIGREEN = “COLORLESS”
RED + ANTIRED
= “COLORLESS”
BLUE + ANTIBLUE
= “COLORLESS”
Color of Gluons
rb
rg
bg
br
Each of the 8 color combinations
have a “color” and an “anti-color”
When quarks interact, they
“exchange” color charge.
gb
gr
rr + gg − 2bb
rr − gg
rg
Don’t
worry
about
what this
means
Quark
1
rg
rg
Quark
2
Color & the Strong Force
Flow of Color Charge
rg
rg
rg
Emission of Gluon
Initially
RED
(quark)
After gluon emission
è
RED-ANTIGREEN
(gluon)
+ GREEN
(quark)
Re-absorption of Gluon
Before gluon absorption
RED-ANTIGREEN + GREEN è
(gluon)
(quark)
After gluon absorption
RED
(quark)
Color Exchange
Quarks interact by the exchange of a gluon.
Since gluons carry color charge, it is fair to say
that the interaction between quarks results in the
exchange of color charge (or just color) !
Gluons – Important Points
q Gluons are the “force carrier” of the strong force.
q They only interact with object which have color,
or color charge.
q Therefore, gluons cannot interact with leptons
because leptons do not have color charge !
q
e+
g
e-
q
This cannot happen, because
the gluon does not interact with
objects unless they have color
charge!
Feynman Diagrams for
the Strong Interaction
qAs before, we can draw Feynman diagrams to represent the
strong interactions between quarks.
q The method is more or less analogous to the case of EM
interactions.
q When drawing Feynman diagrams, we don’t show the
flow of color charge (oh goody). It’s understood to be
occurring.
q Let’s look at a few Feynman diagrams…
Feynman Diagrams (Quark Scattering)
q
q
Quark-antiquark
Annihilation
q
Quark-quark
Scattering
Could also be
Quark-antiquark
Scattering
or
Antiquark-antiquark
Scattering
g
q
q
q
g
q
q
time
Where do we get quark and
antiquarks from?
Quarks
u
d
PROTON
u
And,
antiquarks?…
u
d
ANTIPROTON
u
Flashback to EM Interactions
Recall that photons do not interact with each other.
Why?
Because photons only interact with objects which have
electric charge, and photons do not have electric charge !
γ
γ
γ
γ
γ
This can’t happen
because the photon
only interacts with
electrically charged
objects !
BUT GLUONS DO !!!
Gluons carry the
“charge” of the strong
force, which is
“color charge”, or just
“color” !
Ok, so here’s where it
gets hairy!
Since gluons carry “color charge”,
they can interact with each other !
(Photons can’t do that)
Gluon-gluon Scattering
Gluon-gluon Fusion
g
g
g
g
g
g
g
g
g
g
And quark-gluon interactions as well!
Since both quarks and gluons have color, they can interact with
each other !!!
Quark-Antiquark
Annihilation
Quark-gluon Scattering
q
q
q
g
g
g
g
g
q
g
Where do the gluons come from ?
qThe gluons are all over
inside hadrons!!
Proton
q In fact there are a lot more
than shown here !!!
u
d
q Notice sizes here:
In fact quarks are < 1/1000th
of the size of the proton, so
they are still too big in this
picture !
~10-15 [m]
q Even protons and neutrons
are mostly empty space !!!
u
Confinement
Since the strong force increases as quarks move apart,
they can only get so far…
The quarks are confined together inside hadrons.
Hadron jail !
Hadronization
As quarks move apart, the potential
energy associated with the “spring”
increases, until its large enough, to
convert into mass energy
(qq pairs)
Hadrons!
u
u
u
u
u
u
u
d
s
s
u
u
d
d
In this way, you can see that quarks
are always confined inside hadrons
(that’s CONFINEMENT) !
ΚΚ+
π-
d
d
d
d
π0
What holds the nucleus together?
The strong force !
q Inside the nucleus, the attractive strong force is stronger than
the repulsive electromagnetic force.
q Protons and neutrons both “experience” the strong force.
q The actual binding that occurs between proton-proton and
proton-neutron is the residual of the strong interaction.
Food for thought
Recall: Mass of Proton
~ 938 [MeV/c2]
Proton constituents:
2 up quarks:
2 * (5 [MeV/c2]) = 10 [MeV/c2]
1 down quark:
1 * 10 [MeV/c2] = 10 [MeV/c2]
Total quark mass in proton: ~ 20 [MeV/c2]
Where’s all the rest of the mass ?????
It’s incorporated in the binding energy
associated with the gluons !
è ~98% of our mass comes from glue-ons !!!!
Summary (I)
q The property which gives rise to the strong force is “color charge”
q There are 3 types of colors, RED, GREEN and BLUE.
q Quarks have color charge, and interact via the mediator of the
strong force, the gluon.
q The gluon is massless like the photon, but differs dramatically
in that:
q It has color charge
q It’s force acts over a very short range (inside the nucleus)
Summary (II)
q Because gluons carry color charge, they can interact
among themselves.
q Quarks and gluons are confined inside hadrons because of
the nature of the strong force.
q Only ~50% of a proton’s energy is carried by the quarks. The
remaining 50% is carried by gluons.
q We learn about the strong force by hadron-hadron scattering
experiments.
Right after the Big Bang, particles called quarks unite in groups of three to form the first nucleons:
neutrons and protons.
Action Verbs
A Project LA Activity
jump
What is an action verb?
• A verb is one of the most important
parts of the sentence. It tells the
subjects actions, events, or state of
being. It is always found in the
predicate of a sentence. A verb
that shows action is called an
action verb.
The words are action verbs:
ran
coughed
swallowed
ride
sang
awake
Can you find the action verb in each
sentence?
1. The girls danced in the recital.
2. Our mailman drove a funny car
last week.
3. His teacher wrote the answers on
the board.
4. Alice worked on her homework
Move On
last night.
No, try again.
Yes, that word is an action verb!
Try another sentence
Move On
Present verbs
• An action verb that describes an
action that is happening now is
called a present tense verb.
verb
The bird flies
through the sky.
Flies is a present tense verb
because it is happening right
now.
Present tense verbs
• Many present tense verbs end
with s, but some end with es
es, or
ies.
ies
cries
ies
sleepss
splashes
es
Past Verbs
• Verbs which tell about actions
which happened some time ago are
past
tense
verbs.
The
dog
wanted
a
bone.
Wanted is a past tense verb
because the action has
already happened.
Past tense verbs
• Many past tense verbs end with
ed, but some end with d, or ied
ied.
tried
clapped
played
Future Verbs
• Verbs which tell about actions
which are going to happen are
future
verbs.
We
will tense
awaken
at six
a.m.
Will awaken is a future tense
verb because the action has not
yet happened.
Future tense verbs
• Future tense verbs use special
words to talk about things that
will happen: will, going to,
shall, aim to, etc.
going to start
will enjoy
shall email
Helping Verbs
• A helping verb works with a main verb to
help you understand what action is taking
place.
Elmer was
using the
computer.
23 Helping Verbs
do
may be
might being does
must been did
am
are
is
was
were
(main) (main)
should have
could had
would has
(main)
will
can
shall
Helping Verbs
Other things to keep in mind:
•Not every sentence will have a
helping verb with the main verb.
•When you see an "ing" verb such
as "running", be on the lookout for
a helping verb also.
Helping Verbs
•Sometimes there is another word
which separates the helping verb
from the main verb. One common
example is "not", as in: The boy
couldn't find his socks. The helping
verb is could and the main verb is
find.
Helping Verbs
•A sentence may contain up to three
helping verbs to the main verb. An
example would be: The dog must
have been chasing the cat. The
helping verbs are: must, have, and
been; the main verb is chasing.
Online Verb Games
HitTake
the Back
ArrowQuiz
on your browser to return.
Dave’s
Helping Verb Quiz
Print and complete the Action Verb
Worksheet
Find the Verb Game
Jeopardy Challenge Board
Present and Past Tense Matching Game
Verb Machine
More Verb Activities
•
•
•
•
Irregular Verb Worksheet
Verb Concentration Game
ANTS PICNIC (Irregular Verb Game)
Verb Worksheet
MAIN
Putting it all together
What IS Matter ?
• Matter is all the “stuff” around you !
• Here’s the picture we’ve uncovered
Matter
Hadrons
Baryons
Mesons
Quarks
Anti
Anti-Quarks
Quarks
Leptons
Charged Neutrinos
Forces
Gravity
Weak
Strong
EM
The Quarks
Family
Quark Charge
Mass
[MeV/c2]
Quark
Charge
Mass
[MeV/c2]
1
d
-1/3
~10
u
+2/3
~5
2
s
-1/3
~200
c
+2/3
~1500
3
b
-1/3
~4500
t
+2/3 ~175,000
Ø Each quark has a corresponding antiquark.
Ø Antiquarks have opposite charge to their quark.
Ø Huge variation in the masses, from 5 [MeV/c2] to 175,000 [MeV/c2].
The Leptons
Family Charged Charge
Mass
[MeV/c2]
Neutral
Charge
Mass
[MeV/c2]
eµ−
τ−
~0.51
~105
~1780
νe
νµ
ντ
0
0
0
~0
~0
~0
1
2
3
-1
-1
-1
Ø Each lepton has a corresponding anti-lepton.
Ø Antileptons have opposite charge to their lepton.
Ø Huge variation in the masses, from 0.5 [MeV/c2] to 1,780 [MeV/c2].
Forces
q Forces are the due to the exchange of force carriers.
q For each fundamental force, there is a force carrier
(or set of them).
q The force carriers only “talk-to” or “couple to”
particles which carry the proper charge.
Electromagnetic: the photon (γ)
Electric Charge (+, -)
Strong:
the gluon (g)
Color Charge (r,g,b)
Weak:
the W+, W- & Z0
Weak Charge
Particles & Forces
quarks
Charged
leptons
(e,µ,τ)
Neutral
leptons
(ν)
Color
Charge ?
Y
N
N
EM
Charge ?
Y
Y
N
Weak
Charge ?
Y
Y
Y
q Quarks can participate in Strong, EM & Weak Interactions !
q All quarks & all leptons carry weak charge
In other words…
q Since quarks have color charge, EM charge & weak charge,
they can engage in all 3 types of interactions !
q Charged leptons (e,µ,τ) carry EM and weak charge, but no
strong charge. Therefore, they can participate in the EM & weak
interaction, but they cannot participate in the strong interaction.
q Neutrinos only carry weak charge, and therefore they only
participate in the weak interaction è they can pass through the
earth like it wasn’t even there !
Why should we believe that forces
are the result of force carriers?
q The Standard Model (SM) which I have describe to you is just that,
it’s a model, or better yet, a theory.
q All forces are described by exchange of force carriers, period !
q It’s is an extremely successful theory.
q It explains all subatomic phenomenon to extraordinary precision!
One example is in a quantity referred to as the electron’s “g-factor”
“g” from experiment:
“g” from theory (SM):
2.0023193043768
2.0023193043070
They agree to better than 1 part in 10 billion ! Coincidence ?
Particle or Wave?
Two benchmark experiments established the foundation for the
particle nature of light
1. Photoelectric Effect
2. Compton Effect
Both experiments indicated that light was acting like a particle
with energy and momentum given by:
E = hν
= hc / λ
p = E / c = (hc / λ) / c
=h/λ
Uses
c = λν
q This light particle has energy and momentum, but no mass !!!
q It’s energy & momentum are inversely proportional to the wavelength
Photoelectric Effect
“Classical” Method
What if we try this ?
Increase energy by
increasing amplitude
Vary wavelength, fixed amplitude
electrons
emitted ?
No
No
No
No
electrons
emitted ?
No
Yes, with
low KE
Yes, with
high KE
No electrons were emitted until the frequency of the light exceeded
a critical frequency, at which point electrons were emitted from
the surface!
(Recall: small λ è large ν)
The Electromagnetic Spectrum
Shortest wavelengths
(Most energetic photons)
E = hν = hc/λ
h = 6.6x10-34 [J*sec]
(Planck’s constant)
Longest wavelengths
(Least energetic photons)
The EM force and the Photon
q The photon is the carrier of the EM force.
q It can only “talk-to” particles which have electric charge.
q A photon does NOT have electric charge, and therefore it
cannot interact with other photons
q While the photon is massless, it does carry both momentum
& energy given by:
p=h/λ
E = pc = hc / λ = hν
q When charged particles exchange photons, they are exchanging
this momentum. One particle emits the photon & the other absorbs it !
q Can also have particle-antiparticle annihilation into a photon.
Electromagnetic Force
Quark Pair
Production
e+
e-
q
γ
q
Detectable
hadrons,
such as
π+, π-, π0,
p, n, etc
Electron – Proton Collision !
e
e
u
u
hadrons
Proton
u
d
e-
hadrons
eγ
u
u
d
u
This the Feynman diagram for an
electron scattering off an up quark !
Actual e+e- Collision at Cornell’s Collider
e + + e − → qq → hadrons
E ~ 5 [GeV] for
the e+ and eHadrons
which are
charged
and are “bent”
by a magnetic
field
Side view of
Detector
Event
is not
balanced…
Probably a ν in
this interaction
ν?
Another e+ e- Collision at CERN
+
−
e + e → qq
LOTS
MORE
HADRONS !!!
→ hadrons
E ~ 103 [GeV] for
the e+ and e-
How much energy is needed to produce a
t t pair via an e+e- Collision ?
t
e+
Me = 0.5 MeV/c2
Mt = 175 GeV/c2
e-
t
What minimum energy is needed by each incoming particle to produce
the top and antitop quark?
A) 175 MeV
B) 350 GeV
C) 175 GeV
D) 350 MeV
What maximum mass particle can
be produced?
particle
q
Ee = 115 GeV
(each)
q
antiparticle
What maximum mass particle can be created in this collision ?
A) 115 MeV/c2
B) 230 GeV/c2
C) 115 GeV/c2
D) 230 MeV/c2
Strong Force and the Gluon
q The gluon is the carrier of the strong force.
q Unlike the EM force, it gets stronger as quarks separate !
q It can only “talk-to” particles which have color charge (quarks).
q Since gluons do have color charge, they can interact with
other gluons !
q The gluon is also massless.
q When quarks exchange gluons, they are exchanging color charge.
One quark emits the gluon & the other absorbs it !
q Quarks and antiquarks can annihilate into a gluon!
Color (or Color charge)
ØLike electric charge, quarks have an internal property which
allows gluons to interact with them (i.e., couple to them).
ØThis property is called color. Quarks can have one of three colors:
red, green, or blue.
Ø Antiquarks have anticolor: antired, antigreen or antiblue.
Ø Gluons also carry color (r b, b g, g r, etc ), and therefore can
interact among themselves !!! This is the most striking difference
between gluons & photons!
Ø FYI, it is the fact that gluons have color which leads to confinement
Hadrons
q Because of the strong force, quarks are bound into hadrons.
q Hadrons are simply particles which interact via the strong force.
q Our inability to directly observe the color of hadrons have lead
us to believe that all hadrons are colorless
q There are two types of hadrons:
Baryons: bound state of any 3 quarks (except the top quark)
( 1 red + 1 green + 1 blue == colorless )
Mesons: bound state of a quark and antiquark (except t)
one color + one anticolor ( r r, g g, or b b ) == colorless )
q Antibaryons contain 3 antiquarks
Proton-Proton Collision
hadrons
u
u
u
d
u
u
hadrons
d
u
u
u
u
u
u
d
u
u
u
u
d
u
d
u
u
d
u
d
u
u
d
u
hadrons
d
u
u
d
d
hadrons
d
The up & down
quarks have exchanged
a gluon, and hence
underwent an interaction!
Quark-Quark Interaction
to
hadrons
d
u
u
to
hadrons
u
u
g
d
u
u
d
d
to
hadrons
to
hadrons
Quark-Gluon Interaction
d
u
u
to
hadrons
to
hadrons
g
g
g
d
u
u
d
d
to
hadrons
to
hadrons
Hadronization
As quarks move apart, the potential
energy associated with the “spring”
increases, until its large enough, to
convert into mass energy
(qq pairs)
Hadrons!
u
u
u
u
u
u
u
d
s
s
u
u
d
d
In this way, you can see that quarks
are always confined inside hadrons
(that’s CONFINEMENT) !
ΚΚ+
π-
d
d
d
d
π0
p p à t t from Fermilab
Jet = spray
of particles
when a quark
undergoes
hadronization
4 jets è 4 quarks
emerging from
the interaction.
Putting it all together
The Carriers of the Weak Force
qThree force carriers for the weak force: W+, W- and Z0
q The W+ and W- are the ones I have emphasized, and their role
in the decay of heavy quarks to lighter quarks.
q The W+ and W- carry both electrical and weak charge.
qThey “connect” the +2/3 charge quarks with the –1/3 charge
quarks (a change in charge of 1 unit).
q These range of the weak force is very short !! It’s about 10-18 [m],
which is about 10,000 times smaller than the range of the strong force
Particles & Forces
quarks
Charged
leptons
(e,µ,τ)
Strong
Y
N
N
ElectroMagnetic
Y
Y
N
Y
Y
Y
Weak
Neutral
leptons
(ν)
Quarks carry strong, weak & EM charge !!!!!
Weak Force
qThey W and Z particles can only“talk-to” particles which have
weak charge (the leptons and the quarks !).
q Heavy quark decay to lighter quarks via emission of a
W+ or W-.
q The weak force is also responsible for neutron decay.
q Because the weak force is sooo weak, neutrinos can pass
through matter (like the earth) as if it wasn’t there !
q Quarks and leptons can interact by exchanging a W or Z
force carrier…
Neutron Decay (cont)
u
d
d
Neutron
n
u
u
d
+
W-
Proton
p
+
e-
+
νe
e-
+
νe
+
νe
But in fact, what’s really going on is this:
d
u
+
e-
What about the decay of a b-quark?
−
b à c + µ + νµ
νµ 0
µ-
-1
Wb
c
-1/3
+2/3
Notice: Here, the W- decays to a µ− and νµ,could have also been a
e−νe, or τ−ντ
b-quark decay at the hadron level
Decay of a B- Meson
Could end up as:
B- à D0 π−
u
W-
B-
b
u
B- à D0 π−π0
d
c
0
D
u
B- à D0 π− π+ π−
etc
qAdditional particles are created when the strong force produces more
quark-antiquark pairs. They then combine to form hadrons!
q Notice that the charge of the particles other than the D0 add up to the
charge of the W- (Q = -1), as they must!
Hadronization – Producing hadrons!
Hadrons!
u
u
π0
u
u
u
u
d
π-
d
d
d
In this way, you can see that quarks
are always confined inside hadrons
(that’s CONFINEMENT) !
uu pair produced by converting
energy stored in the “stretched
spring” into mass energy…
Conservation Laws
q Conservation of Total Energy
q Conservation of Total Momentum
q Conservation of Electric Charge
q Conservation of Baryon Number
q Conservation of Lepton Number (Le, Lµ, and Lτ)
Energy Conservation (I)
A+B à C +D
q Energy conservation means:
Energy of particle “A” + Energy of particle “B”
= Energy of particle “C” + Energy of particle “D”
q Or, in simpler notation,
EA + EB = EC + ED
If you knew any 3 of the energies, you could compute the fourth!
è So, in such a reaction, you only need to measure 3 particles, and
energy conservation allows you to compute the fourth!
Energy Conservation (II)
Decay Process: A à B + D
If particle A has non-zero mass (mA > 0), then:
mB < mA
mD < mA
This is a consequence of energy conservation (see lecture 24) !
B
D
A
EB=MBc2
B
EA=MAc2
A
ED=MDc2
D
This can’t
happen if
MB>MA, or
MD>MA
This can
happen
Interaction – Conversion of KE to Mass
π0
n
π+
p
π0
p
p
p
p
ππ0
n
p
Notice that the total mass of the particles after the interaction is
larger than the incoming masses (2 proton masses) !
This is OK, as long as the incoming protons have enough kinetic
energy to produce all these particles
Then why can’t this happen in decays?
Well, according to me, this
neutron is at rest !
So, ha !
Therefore it cannot decay
to something heavier!!
That would violate energy
conservation !
n
Now, if the neutron is zipping along, and it has a lot of KE,
why can’t it decay to something heavier by converting some
of its KE into mass ???
Momentum Conservation (I)
e+
e-
(I) If this electron & positron have equal & opposite velocity, what
can be said about their total momentum?
A) It’s twice as large
B) It’s zero
C) It’s negative
D) It’s positive
Bam
(II) What can be said about the total momentum of all the particles
which are produced in this collision at top?
A) It’s positive
B) It’s negative
C) It’s same as in (I)
D) It’s 0.5 [MeV/c]
Momentum Conservation (II)
neutron at rest appears to
decay to a proton + electron
p
n
ν
e
mP
me
Since both the electron and proton are both moving off to the
right, their total momentum cannot be zero.
è In other words, this reaction, as shown cannot occur,
since it would violate momentum conservation.
This is precisely what lead to the conjecture that there must be
an undetected particle, called the neutrino!
Charge Conservation
Consider the process:
π+ + p à n + π0
Can it occur?
What about this one ?
π+ + n à p + π0
What about this one ?
π+ + p à π0 + π0
Total charge on left has to equal total charge on right in order for
charge to be conserved! The process could still be forbidden to occur
if it violates some other conservation law !
Baryon Number Conservation
Rules of the game:
For each baryon,
assign B = +1
For each antibaryon, assign B = -1
Compare total Baryon number on left side to right side…
Y
N
π+ + p à π0 + π0
X
p + p à p + π+ + n + π0
X
n à π0 + π0
X
n àp+p
X
p + p à n + n + π+ + π−
X
Why can’t the proton decay ?
pà?+?+?
Since baryon number must be conserved , there MUST BE a
baryon among the “?” decay products.
But, the proton is the lowest mass baryon (938 [MeV/c2]).
So there is nowhere it can go !
It CANNOT decay into something heavier, as this would violate
energy conservation !
p
938
[MeV/c2]
à
<
n
+
e+
+
νe
940
+
0.51 +
~0
[MeV/c2]
[MeV/c2] [MeV/c2]
Lepton Number Conservation
A+B à C +D
At it’s heart, it’s just:
Total lepton number on LHS = Total lepton number on RHS
All leptons get assigned:
L = +1
All antileptons get assigned: L = -1
But, it’s more powerful than that !
It can be applied for “electron-type”, “muon-type” and “tau-type”
objects separately!
Example
Photon Conversion: γ à e+ + µLepton
Antilepton
q If we don’t distinguish between “electron-type” and “muon-type”
objects, we would conclude that this process can occur, since
we have a lepton and anti-lepton on the RHS !
q If we require both Le and Lµ conserved separately, we see that
this process violates both è cannot occur !
And, in fact this process is never observed…
γ à e+ + µLe
Lµ
0
0
-1
0
0
1
X
X
Example II
n
à
p
+
e+
+
νµ
Energy
(Check
mass)
940
[MeV/c2]
938
[MeV/c2]
0.51
[MeV/c2]
~0
[MeV/c2]
Charge
0
-1
+1
0
Baryon
Number
-1
-1
0
0
Le
0
0
-1
0
Lµ
0
0
0
+1
The Big Bang !
Everything that could have possibly existed, did exist !
ss
νe
e−
ντ
νµ
cc
+
µ+
τ
dd
uu
τ
µ−
−
tt
bb
ντ
νµ
e
+
νe
And ???
Matter today
q Today, the universe is a relatively cold place (remember
the 3o microwave background… that’s –270 oC)
q Nearly all heavy quarks have decayed through the weak
interaction into up & down quarks.
tàbàcà sàu
àd
q The up & down quarks which are the lightest of the quarks are the
lightest, and have combined to form protons & neutrons
q The protons and neutrons have combined with electrons to form
our atomic elements…and hence, US !
q The heavy quarks are produced in cosmic rays or at large accelerator
laboratories, like Fermilab..
Space is mostly “empty space”
Atoms are > 99.999% empty space
Electron
γ
Nucleus
Protons & Neutrons are > 99.999%
empty space
g
u
Proton
u
The quarks
make up a negligible
fraction of the
protons volume !!
d
The Universe
The universe and all the
matter in it is almost all
empty space !
(YIKES)
So why does matter appear to
be so rigid ?
Forces, forces, forces !!!!
It is primarily the strong and electromagnetic forces which
give matter its solid structure.
Strong force è
defines nuclear size
Electromagnetic force è
defines atomic sizes
So why is this stuff
interesting/important?
qAll matter, including us, takes on its shape and structure
because of the way that quarks, leptons and force carriers
behave.
q Our bodies, and the whole universe is almost all empty space !
q By studying these particles and forces, we’re trying to get
at the question which has plagued humans for millenia …
How did the universe start? And how did we emerge from it all?