Download Pre-class 11

Announcements
Review: Relativistic mechanics
• Reading for Monday: Chapters 1 & 2!
• HW 4 due Wed. Do it before the exam!
• Exam 1 in 4 days. It covers Chapters 1 & 2.
Room: G1B30 (next to this classroom).
Relativistic momentum:
p≡m
Relativistic force:
F≡
Total energy of a
particle with mass ‘m’:
dr
dt propper
= γ mu
dp d
= (γ m u )
dt dt
Etot = γmc2 = K + mc2
• Practice exam available on CUlearn.
(NOTE: our exam will be all multiple choice)
These definitions fulfill the momentum and energy
conservation laws. And for u<<c the definitions for p, F,
and K match the classical definitions. But we found that
funny stuff happens to the proper mass ‘m’.
From last class: total energy
E = γmc2 = K + mc2
v
-v
m
m
Etot = 2K + 2mc2
m
m
Etot = Mc2
Mc2 ≡ 2K + 2mc2
M > 2m
Example: Deuterium fusion
Example: Deuterium fusion
Isotopes of Hydrogen:
Isotope mass:
Deuterium: 2.01355321270 u
Helium 4: 4.00260325415 u
(1 u ≈ 1.66—10-27 kg)
1kg of Deuterium yields ~0.994 kg of Helium 4.
Energy equivalent of 6 grams:
E0 = mc2 = (0.006 kg)·(3·108 m/s )2 = 5.4·1014 J
Enough to power ~20,000 American households for 1 year!
Relationship of Energy and momentum
Recall:
= γmc2
p = γmu
Total Energy: E
Momentum:
From the momentum-energy relation E2 = p2c2 + m2c4
we obtain for mass-less particles (i.e. m=0):
Therefore: p2c2 = γ2m2u2c2 = γ2m2c4 · u2/c2
use:
u2 γ 2 − 1
= 2
c2
γ
p2c2 = γ2m2c4 – m2c4
E = pc , (if m=0)
p=γmu and E=γmc2 p/u = E/c2
=E2
This leads us the momentum-energy relation:
or:
Application: Massless particles
E2 = (pc)2 + (mc2)2
E2 = (pc)2 + E02
Using E=pc leads to:
u=c
, (if m=0)
Massless particles travel at the speed of light!!
C no matter what their total energy is!!
Example:
Electron-positron annihilation
Do neutrinos have a mass?
Positrons (e+, aka. antielectron) have exactly the same mass
as electrons (e-) but the opposite charge:
me+ = me-= 511 keV/c2 (1 eV ≈ 1.6—10-19J)
Neutrinos are elementary particles. They come in three
flavors: electron, muon, and tau neutrino (νe,νµ, ντ). The
standard model of particle physics predicted such particles.
The prediction said that they were mass-less.
E1, p1
eBAM!
e+
E2, p2
At rest, an electron-positron pair has a total energy
E = 2 — 511 keV. Once they come close enough to each
other, they will annihilate one other and convert into two
photons.
What can you tell about those two photons?
Do neutrinos have a mass? (cont.)
The fusion reaction that takes place in the sun (H + H He)
produces such νe. The standard solar model predicts the
number of νe coming from the sun.
All attempts to measure this number on earth revealed only
about one third of the number predicted by the standard
solar model.
Summary SR
• Classical relativity Galileo transformation
Bruno Pontecorvo predicted the ‘neutrino oscillation,’ a
quantum mechanical phenomenon that allows the neutriono
to change from one flavor to another while traveling from the
sun to the earth.
Why would this imply that the neutrinos have a
mass?
• Special relativity (consequence of 'c' is the same in all inertial
frames; remember Michelson-Morley experiment)
– Time dilation & Length contraction, events in
spacetime Lorentz transformation
– Spacetime interval (invariant under LT)
– Relativistic forces, momentum and energy
– Lot's of applications (and lot's of firecrackers)
C
Everything we have discussed to this point will be part of the first
mid-term exam (including reading assignments and homework.)
If you have questions ask as early as possible!!
Part 2: Quantum* Mechanics
Quantum Mechanics is the greatest
intellectual accomplishment of human race.
- Carl Wieman, Nobel Laureate in Physics 2001
To understand something means to derive it from
quantum mechanics, which nobody understands.
-- - unknown origin…
Courtesy of IBM
*We say something is quantized if it can occur only in certain discrete amounts.
Part 2 of this course:
1. Basic properties of light (electromagnetic waves).
2. Photoelectric effect and how it shows light comes in
quantum units of energy. When is a wave not a wave?
(If it is a particle!)
2. Atomic spectra- quantized energy of electrons in atoms.
3. Bohr model of the atom. Where it works. Why it is wrong.
4. de Broglie idea- wave-particle duality of electrons etc.
When is a particle not a particle?
(when it’s a wave).
5. Schrodinger Equation and quantum waves.
6. What they are, how to use.
7. Applications: chemistry, electronics, lasers, MRI, C
Properties of light Interaction with matter
Rest of today (and next class):
Basic properties of light (aka. electromagnetic
waves):
– How to generate light
– Wave-like properties of light
– Next week: Particle-like properties of light
Disclaimer: A very exciting part of this course is the
particle-wave duality of light (and matter!) However, do
not get confused with when to use the wave or the
particle representation of the very same physical entity.
It actually depends on the experiment (‘question’ or
‘measurement’)! We will see several experiments that
should help you understand this concept.
Strap in and enjoy the ride!
The sun produces lots of light
Electric fields exert forces on charges
(e’s and p’s in atom)
+
+
+
+
+
+
+
+
E
+
_
F=qE
E
F=qE
-
Why? How?
Force = charge • electric field
F= qE
+ +
+
Light is an oscillating E(and B)-field. It interacts with matter by
exerting forces on the charges
– the electrons and protons in atoms.
+
Surface of sun- very hot!
Whole bunch of free electrons
whizzing around like crazy. Equal
number of protons, but heavier so
moving slower, less EM waves
generated by protons.
Light is an oscillating E (and B)-field
• Oscillating electric and magnetic field
• Traveling at speed of light (c)
Snap shot of E-field in time:
At t=0
A little later in time
E
c
Emax
Remember this one?
Electromagnetic
radiation
E-field (for a single color):
E(x,t) = E0 sin(2πx/λ ─ ωt +
This symbolizes a local disturbance
of the electric field E(x,t)
Light source
E
λ
φ)
λ = 2πc/ω, ω = 2πf = 2π/T
E0
x
x
φ
Wavelength λ of visible light
is: λ ~ 350 nm C 750 nm.
E
The E-field is a function of position (x) and time (t):
E(x,t) = Emaxsin(ax+bt)
sin(ax-bt) , (here: b/a=c)
x
B
Electromagnetic Spectrum
Making sense of the Sine Wave
Spectrum: All EM waves. Complete range of wavelengths.
Wavelength (λ) =
Frequency (f) =
distance (∆x) until wave repeats # of times per second E-field at
λ
point changes through complete
Blue light
cycle as wave passes
λ
Red light
λ
Cosmic
rays
CQ: What does the curve tell you?
-For Water Waves?
-For Sound Wave?
-For E/M Waves?
SHORT
Electromagnetic waves carry energy
Emax=peak amplitude
c
Emax
X
E(x,t) = Emaxsin(ax-bt)
Light shines
on black tank
full of water.
How much
energy
absorbed?
LONG
Maxwell’s Equations: Describes EM radiation
dΦ m
Qin
•
=
−
E
d
s
E
•
d
A
=
∫
∫
dt
ε0
∫B•ds = µ I
∫B•d A= 0
0 through
Intensity = Power = energy/time α (Emax)2 α (amplitude of wave)2
area
area
B
Intensity only depends on the E-field amplitude but not
on the color (or frequency) of the light!
E
+ ε 0 µ0
dΦ e
dt
Maxwell’s Equations: Describes EM radiation
Qin
∫E •d A=
ε0
∫B•d A= 0
In 3-D:
∫E •ds = −
∫B•ds = µ I
1 ∂2E
∇E= 2 2
c ∂t
2
dΦ m
dt
0 through
In 1-D:
Show that E(x,t) = Emaxcos(ax+bt)
+ ε 0 µ0
dΦ e
dt
∂2E 1 ∂2E
=
∂x 2 c 2 ∂t 2
How can we see that light
really behaves like a wave?
During 1600-1800s: lot’s of debate about what light really is.
After ~1876 (Maxwell): Light = EM radiation viewed as a
wave. How can it be tested?
What is most definitive observation we can make that
tells us something is a wave?
is a solution (in 1-D)
with b/a=c.
EM radiation is a wave
What is most definitive observation we can
make that tells us something is a wave?
EM radiation is a wave
What is most definitive observation we can
make that tells us something is a wave?
Constructive interference:(peaks are lined up and valleys are
lined up)
c
Destructive interference: (peaks align with valleys E-fields
cancel each other)
c
Two slit interference
Light is a wave interference!
The definite check that light IS a wave
Observe interference!
wave interfarence online
wave-interference_en.jar
wave-interference_en.jar