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
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
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