1.
 REPRESENTED BY
ABDUL SALIM
Govt. Engineering College,
Ajmer
B.Tech(Computer Science)
1st year(2nd semester)
Compton Effect

2.
 Introduction
 Theory
 Compton Shift
 Direction of recoil electron
 Kinetic energy of recoil electron
 Experimental demonstration

3.
Introduction
In 1923, Compton’s Experiment Of X-ray
Scattering From Electrons Provided The
Direct Experimental Proof For Einstein’s
Concept Of Photons.
Einstein’s Concept Of Photons
Photon Energy: E = hv
Photon Momentum P: = E/c = hv/c=h/.
Compton’s Apparatus To Study
Scattering Of X-rays From Electrons
A.H. Compton

4.
THEORY
for elastic collision
Total energy of the = Total energy after
system before collision collision
hv+m₀c²=hv´+mc²
 according to compton
 electron scattered by photon
 collision is elastic
 e gains some kinetic energy & recoil at angle Ф
 photon is recoil at angle θ

5.
e‾P
Collision
Electron at restphoton

6.
e‾P
Collision

7.
e‾P
Collision
Elastic collision
e‾ gain kinetic energy

8.
e‾
P
Collision
Elastic collision
Θ
Ф

9.
e‾
P
Collision
Θ
Ф

10.
e‾
P
Collision
Θ
Ф
E′=hv′
P=hv′/c
K.E=mc²
P=mv

11.
Derivation
For elastic collision
According to momentum conservation along the direction of incident photon;
hv/c + 0 = hv´cosθ/c + mvcosΦ
Perpendicular to the direction of incident photon;
0 = hv´sinθ/c - mvsinΦ
h(v - v´) + m₀c² = mc²
m = ___m₀____
√1-v²/c²
    cos12
 hhhhcme

12.
Continuing on
And using v=c/λ we arrive at the Compton effect
And h/mc is called the Compton wavelength
)cos1(2






cm
h
e
  cos1
cm
h
e
m
cm
h
e
C
12
1043.2 


13.
Summarizing and adding a few other useful results are
 
 























2
tan1cot
cos11
cos1
2
2






cm
hv
hhT
cm
hv
hv
h
cm
h
e
e
e
e
Total kinetic energy

14.
Kinetic Energy of Recoil Electron
According to energy conservation law
K.E = hv - hv´ = hv(1 - v´/v)
v´ 1
V 1 + α(1 – cosθ)
2hvαsin²θ/2
1 + 2αsin²θ/2
K.E =
α = hv/m₀c²
When θ = π(Back scattering)
(K.E)max = 2αhv/(1+2α)
When θ = π/2
K.E = hvα/(1+α)
When θ = 0 (No scattering)
K.E = 0

15.
Direction of recoil electron
mvcsinΦ hv´sinθ
mvccosΦ hv - hv´cosθ
= =tanΦ
sinθ
v/v´ - cosθ
tanΦ = = sinθ
(1+α)(1 – cosθ)
cotθ/2
1 + hv/m₀c²
tanΦ =

16.
Special case
When θ=0
cos 0 =1
∆λ=λ˛(1 - cos θ) = 0
When θ=π/2
cos π/2 = 0
∆λ=λ˛(1 - cos θ) = λ˛
When θ=π
cosπ= -1
∆λ=λ˛(1 - cos θ) =2λ˛
No scattering
Scattering
perpendicular
Back scattering

17.
Results of Compton’s scattering experiment

18.
 Experimental intensity-versus-
wavelength plots for four
scattering angles .
 The graphs for the three nonzero
angles show two peaks, one at 0
and one at ’ > 0.
 The shifted peak at ’ is caused
by the scattering of x-rays from
free electrons.
 Compton shift equation:
Compton’s prediction for the
shift in wavelength
’ - 0 = (h/mec)(1 – cos ).
 h/mec = 0.00243 nm

19.
Thank You