Download Chapter 29 - Wayne State University Physics and Astronomy

General Physics (PHY 2140)
Lecture 21
 Modern Physics
Elementary Particles
Strange Particles – Strangeness
The Eightfold Way
Quarks
Colored Quarks
Electroweak Theory – The Standard Model
The Big Bang and Cosmology
Chapter
Chapter 2930
http://www.physics.wayne.edu/~alan/2140Website/Main.htm
Previously…
 Nuclear Energy, Elementary Particles
 Nuclear Reactors, Fission, Fusion
 Fundamental Forces
 Classification of Particles
Elementary Particles
 First we studied atoms
 Next, atoms had electrons and a nucleus
 The nucleus is composed of neutrons and
protons
 What’s next?
30.5 The Fundamental Forces in Nature
 Strong Force
 Short range ~ 10-15 m (1 fermi)
 Responsible for binding of quarks into neutrons and protons
 Gluon
 Electromagnetic Force




10-2 as strong as strong force
1/r2 force law
Binding of atoms and molecules
Photon
 Weak force
 ~ 10-6 times as strong as the strong force
 Responsible for beta decay, very short range ~10-18 m
 W+, W- and Z0 bosons
 Gravitational Force
 10-43 times as strong as the strong force
 Also 1/r2 force law
 Graviton
30.8 Particle Classification
(Classify the animals in the particle zoo)
Hadrons (strong force interaction, composed of quarks)
 We already met the mesons (middle weights)
 Decay into electrons, neutrinos and photons
 Baryons, i.e. the proton and neutron (the
heavy particles)
 Still other more exotic baryons:
 L, S, X,  all are heavier than the proton
 Decay into end products that include a proton
Particle Classification – cont.
 Leptons
 Small or light weight particles
 Are point like particles – no internal structure
(yet)
 6 leptons
 Electron e, muon m, tau t
 and their associated neutrinos: ne, nm, nt
 Also, their antiparticles
 Neutrinos have tiny mass, ~3 eV/c2
Some members of the Zoo
Particle Physics Conservation Laws
So far in Physics we have conservation of energy,
momentum (linear and angular), charge, spin.
Now we add more to help balance particle
reactions
 Baryon number:
 B = +1 for baryons, -1 for anti-baryons
 Eg. Proton, neutron have B = +1
 p, n , antiparticles have B = -1
 B = 0 for all other particles (non-baryons)
More Conservation Laws
 Lepton number
 L = +1 for leptons, -1 for anti-leptons
 L = 0 for non-leptons
 Example for electrons:
 Electron e, electron neutrino ne have Le = +1
 Anti electron and antineutrino have Le = -1
 Other leptons have Le = 0 BUT have their own lepton
numbers, Lm, Lt
 Refer to table 30.2
Example neutron decay
 Consider the decay of the neutron
n  p + e + νe
+
-
 Before: B = +1, Le = 0
 After: B = +1, Le = +1 -1 = 0
Quiz 30.2
 Which of the following cannot occur?
 (a)
p+p  p+p+p
 (b)
n  p + e + ne
 (c)
μ  e + n e + νμ
 (d)
π  μ +νμ
-
-
-
-
Quiz 30.2 - answer
 The disallowed reaction is (a) because
 Charge is not conserved:
 Q = +2  Q = +1
 Baryon number is also not conserved:
 B = +2  B = +2-1 = +1
p+p  p+p+p
Strangeness
 Several particles found to have unusual
(strange) properties:
 Always produced in pairs
p- + p+  K0 + L0 but not p- + p+  K0 + n
 Decay is slow (indicative of weak interaction
rather than strong) Half-lives of order of 10-10
to 10-8 sec
 Members of the strange club: K, L, S
More Strangeness
 Explanation lies in the addition of a new
conservation law – Strangeness, S
 One of the pair of strange particles gets
S=+1 the other S=-1. All other particles
get S=0. So in the previous reaction,
strangeness is conserved:
 Before S=0; After S=+1-1 = 0
 Second reaction violates strangeness
Example 30.6: Strangeness Conservation
Consider:
p- + n  K+ + S-
 Before: S=0+0=0 (no strange particles)
 After: K+ has S=+1, S- has S = -1 thus the
net strangeness S = +1-1 = 0
 So reaction does not violate law of
conservation of strangeness, the reaction
is allowed
The Eightfold Way
Consulting table 30.2, Take the first 8
baryons and plot Strangeness vs. Charge.
We get an interesting picture. A hexagonal
pattern emerges.
If we do the same for the spin 0 mesons we
also get a hexagonal pattern.
The Eightfold Way
The Original Quark Model (in B/W)
 Gell-Mann (1961) proposed hadrons have




structure, i.e. composed of a more
fundamental type of particle.
Quarks have fractional charge e/3 or 2e/3
Three types u, d, s: up, down, strange
Mesons were made of 2 quarks: q, q¯
Baryons were made of 3 quarks
But that wasn’ enough!
 Soon after, experimental discrepancies
required the addition of three more quarks
 Top, bottom and charm: t, b, c
 And three more conservation laws: C, B, T for
charm, bottomness and topness
Properties of Quarks and Antiquarks
Fundamental Particles: Properties
Quarks
Particle
Rest Energy
Charge (e)
u
360 MeV
+2/3
d
360 MeV
-1/3
c
1500 MeV
+2/3
s
540 MeV
-1/3
t
173 MeV
+2/3
b
5 GeV
-1/3
Size of quark: < 10-18 m
Fundamental Particles Properties
continued
Leptons
Particle
Rest Energy
Charge
e-
511 keV
-e
m-
107 MeV
-e
t-
1784 MeV
-e
ne
< 30 eV
0
nm
< 0.5 MeV
0
nt
< 250 MeV
0
Quarks in Mesons and Baryons
We should still
be in B/W!
Color
 Because of the Pauli exclusion principle
(all quarks are spin ½ particles) can’t have
three of the same particles occupying the
same state.
 Example: - is (sss) so need three
different yet strange quarks
 So colored quarks were proposed
Color continued
 Three color charges were added
 Red, green blue: r, g, b
 And…three anti-colors
¯ g,
¯ b¯
 antired, antigreen and antiblue: r,
 Mesons have a color anticolor pair
 Spin is either zero or 1 so can have ↑↑ or ↑↓
 Baryons must have three different colors
 Spin is ½ so have ↑↑↓ or ↓↓↑
Quarks combinations with color
Total spin is 0 or 1
Total spin is ½ or 3/2
Quantum Chromodynamics
 In analogy with photons and the electromagnetic





force, an interaction between colored quarks is
the result of color force – 8 colored gluons.
The general theory is complex but explains
experimental results better.
Numerical results can be very hard to calculate
Opposite colors attract, red-antired, in analogy
with electromagnetism.
Different colors also attract though less strongly
Residual color force is responsible for nuclear
force that bind protrons and neutrons.
Interactions in the Yukawa pion and
quark-gluon models
Yukawa’s pion model
Quark QCD model
In both cases a proton-neutron
pair scatter off each other and
exchange places.
The Standard Model
History of the Universe
and of the four forces
Energy: 1028
Time:
0
1024
10-40
10-35
1021
1017
1013
1011
10-11
eV
sec
Time
Big Bang Model
A broadly accepted theory for the origin and
evolution of our universe.
It postulates that 12 to 14 billion years ago, the
portion of the universe we can see today was only
a few millimeters across. It has since expanded
from this hot dense state into the vast and much
cooler cosmos we currently inhabit.
In the beginning, there was a Big Bang, a
colossal explosion from which everything in
the Universe sprung out.
Experimental Evidence of the Big Bang

Expansion of the universe


Abundance of the light elements H, He, Li


Edwin Hubble's 1929 observation that galaxies were generally
receding from us provided the first clue that the Big Bang theory
might be right.
The Big Bang theory predicts that these light elements should have
been fused from protons and neutrons in the first few minutes after
the Big Bang.
The cosmic microwave background (CMB) radiation

The early universe should have been very hot. The cosmic
microwave background radiation is the remnant heat leftover from
the Big Bang.
Cosmic Microwave Background
99.97% of the radiant energy of the
Universe was released within the first
year after the Big Bang itself and now
permeate space in the form of a
thermal 3 K radiation field.
COBE CMB Measurement
• CMB spectrum is that of a nearly perfect blackbody with a temperature
of 2.725 +/- 0.002 K.
• Observation matches predictions of the hot Big Bang theory
extraordinarily well.
• Deviation from perfect black body spectrum less than 0.03 %
• Nearly all of the radiant energy of the Universe was released within the
first year after the Big Bang.
How did we get from there…
… to here?
Let there be light:
400,000-700,000 years
Mini Review

Coulomb’s law
 the superposition principle
F  ke
q1 q2
r2
F

The electric field

0
Flux. Gauss’s law.
Q


EA
cos


 simplifies computation of electric fields net 
o

PE
Potential and potential energy
V  VB  VA 
q
 electrostatic force is conservative
 potential (a scalar) can be introduced as potential
energy of electrostatic field per unit charge
E
q

Equipotential surfaces






They are defined as a surface in space on which
the potential is the same for every point
(surfaces of constant voltage)
The electric field at every point of an
equipotential surface is perpendicular to the
surface
Capacitance and capacitors
1
Q2 1
U  QV 
 CV 2
2
2C 2
Current and resistance
C   0


Capacitors with dielectrics (C↑ if k ↑)
Current and drift speed
Resistance and Ohm’s law

I is proportional to V
Resistivity

material property
A
, C   C0
d
I  nqvd A
V  IR
I
Q
t
RA

l

Current and resistance

Temperature dependence of resistance

Power in electric circuits

R  Ro 1   T  To  
V 

2
P  I V  I R 
R
DC Circuits


V E Ir
EMF
Kirchoff’s rules
I
i 1

Req  R1  R2  R3 
Resistors in series and parallel
n

RC circuit
2
n
i
 0,  Vi  0

i 1
q  Q 1  et / RC
q  Qet / RC
1
1 1
1
 

Req R1 R2 R3

Charging
Discharging

Magnetism









Induced voltages and induction





Magnetic field
Magnetic force on a moving particle
Magnetic force on a current
Torque on a current loop
Motion in a uniform field
Application of magnetic forces
Ampere’s law
Current loops and solenoids
Magnetic flux
Generators and motors
Self-induction
Energy in magnetic fields
AC circuits


F  qvB sin 
F  BIl sin 
F  NBIAsin 
r  mv / qB
 B l  m I
o
  B A  BA cos 
I
E  L
t
Resistors, capacitors, inductors in ac circuits
Power in an AC circuit
Z  R2   X L  X C 
2
X L  XC
tan  
R
L
N
I
1 2
PEL  LI
2
1
XC 
, X L  2p fL
2p fC
 AC circuits
f0 
 Resonance in RLC circuits
 Transformers
 Electromagnetic Waves
v  Vm sin  2p ft   
c
1
2p LC
1
mo o
N2
V2 
V1
N1
 2.99792 108 m s
 Modern physics




Introduction
Gallilean relativity
Michelson-Morley Experiment
Relativity
 Time dilation, length contraction
 Relativistic energy, momentum
 Relativistic addition of velocities
vab 
vad  vdb
v v
1  ad 2 db
c
t 
t p
1 v c
2
p
L  Lp 1  v 2 c 2
2
mv
1 v c
2
2
  mv
KE = mc2 – mc2
 Quantum physics




Blackbody radiation
Planck’s hypothesis
Photoelectric effect
X-rays







Wave function
Uncertainty relations
Atomic Descriptions
Atomic Spectra
Bohr’s Atomic Theory
Quantum Mechanics
Quantum Numbers
maxT  0.2898 102 m  K
En  nhf ,
n  1, 2,3,...
KE  hf  
hc
min 
e  V 
h
xp 
2p
h
E t 
2p
2p r  n , n  1, 2,3,...
Ei  E f  hf
mevr  n , n  1, 2,3,...
 1
1 
 RH  2  2 
 n f ni 



1
 Quantum physics





Electron Clouds (Orbitals)
The Pauli Exclusion Principle
Characteristic X-Rays
Atomic Energy Levels
Lasers and Holography
 Nuclear physics








Nuclear properties
Binding energy
Radioactivity
The Decay Process
Natural Radioactivity
Nuclear Reactions
Medical Applications
Radiation Detectors
A
Z
X
4ke Ze2
d
mv 2
r  r0 A1/ 3
 Nuclear Energy, Elementary Particles




Nuclear Reactors, Fission, Fusion
Fundamental Forces
Classification of Particles – Making sense of the particle zoo
Conservation Laws
Remember:
 Electricity:
 Electric field and electric potential are different things
 Moreover, field is a vector while the potential is a scalar
 Remember the difference between parallel and series
connections
 Remember that formulas for capacitors and resistors are “reversed”
 Magnetism:
 Use right hand rule properly
 Special relativity:
 If the problem involves speeds close to the speed of light, use
relativistic formulas for momentum, energy, addition of velocities
 In particular, KE=mv2/2 is a NONRELATIVISTIC expression for KE
 Atomic and nuclear physics:
 In the way of handling, nuclear reactions are very similar to
chemical reactions
Good Luck on the Final Exam!