Physics 2D Lecture Slides
Week of May 4, 2009
part 1
(Oleg Shpyrko)
Sunil Sinha
UCSD Physics
• X rays are EM waves of low wavelength, high
frequency
q
y ((and energy)
gy) and demonstrate
characteristic features of a wave
– Interference
– Diffraction
• To probe into a structure you need a light source
with wavelength much smaller than the features of
the object being probed
– Good
G d Resolution
R
l ti
Æ λ<< Δ
• X rays allows one probe at atomic size (10-10)m
Compton Scattering : Quantum
Pool !
•
1922: Arthur Compton (USA) proves that X-rays (EM Waves)
have particle like properties (acts like photons)
– Showed that classical theory failed to explain the scattering effect
off
• X rays on to free (not bound, barely bound electrons)
•
Experiment : shine X ray EM waves on to a surface with
almost free electrons
“almost”
– Watch the scattering of light off electron : measure time +
wavelength of scattered X-ray
Compton Effect: what should Happen Classically?
• Plane wave [f,λ] incident
on a surface with loosely
bound electrons
Æinteraction of
E field
of EM wave with electron:
F = eE
• Electron oscillates with
f = fincident
• Eventually radiates
spherical
h i l waves with
ith
fradiated= fincident
– At all scattering angles, Δf &
Δλ mustt be
b zero
• Time delay while the
electron gets a “tan” :
soaks in radiation
Compton Scattering : Setup & Results
Δ λ = ( λ ' − λ ) ∝ (1 − c o s θ )
S c a tte re d λ ' la rg e r th a n in c id e n t
Compton Scattering Observations
Compton Scattering : Summary of Observations
Δλ = (λ -λ ) ∝ ((1 − cos θ ) !
'
Not isotropy in distribution of
scattered radiation
scattered
How does one explain this startling anisotropy?
Compton Scattering: The Quantum Picture
Energy Conservation:
E+m e c 2 = E '+ Ee
Momentum Conserv:
p = p'cosθ +pe cos φ
0 = p'sinθ -p e sin φ
((E − E ') + m c ) = ⎡⎣ p
2
e
2
2
− 2 pp 'cosθ + p '2 ⎤⎦ c 2 + (me c 2 )2
Use these to eliminate
electron deflection
angle (not measured)
E
For light p= ⇒
c
2
2
⎡
⎤ 2
E
EE
'
E
'
2
2
2
E + E ' − 2EE '+
' 2(E − E ')mc
')
= ⎢ 2 − 2 2 cosθ + 2 ⎥ c
c ⎦
c
⎣c
⇒ − EE '+ (E − E ')mc 2 = − EE 'cosθ
⇒
E-E'
1
h
=−
(1
−
cos
θ
)
⇒
(
λ
'−
λ
)
=
(
)(1 − cosθ )
2
EE'
me c
me c
Compton Scattering: The Quantum Picture
Rules of Quantum Pool between Photon and
Electron
h
(λ '− λ ) = (
)(1 − cos θ )
me c
Checking for h in Compton Scattering
It’s the same value for h again !!
Plot scattered photon data, calculate slope and measure “h”
Δλ
( λ '− λ ) = (
h
)(1 − c o s θ )
m ec
Energy Quantization is a
UNIVERSAL characteristic
of energy transactions !
1-cos ϑ
Interference of Waves: A Reminder
Two Identical waves yi ( x, t ) = ymax sin(ki x - ωi t + φi ) travel along +x and interefere
to give a resulting wave y ' ( x, t ). The resulting wave form depends on relative phase difference
between 2 waves. Shown for Δφ = 0, π ,
2
π
3
Read Ch17-8 from Resnick et
al
An X-ray Tube from 20th Century
e
Xray
The “High Energy Accelerator” of 1900s: produced energetic light : X
Ray , gave new optic to subatomic phenomena
X-ray
X
ray Synchrotrons,
Synchrotrons
Argonne National Lab near Chicago
15
Bragg Scattering
photographic film
Bragg Scattering: Probing Atoms
With X-Rays
X-ray
detector
Constructive Interference when net pphase difference is 0, 2π etc
This implied path difference traveled by two waves must be integral
multiple of wavelength : nλ=2dsinϑ
Example : X-Ray Picture of a DNA Crystal and Discovery of
DNA Structure
!
Proteins inside Rhinovirus reconstructed by x-ray diffraction
Other forms of Interaction of Energy Exchange between Radiation and Matter
E mc 2 +mc 2
Always same form of
Matter & Antimatter