MARKING SCHEME FOR ANSWERS TO THE THEORETICAL QUESTION IV Part MARKING SCHEME - THE THEORETICAL QUESTION IV- COMPTON SCATTERING Tota l Sco res IV.
Trang 1MARKING SCHEME FOR ANSWERS TO THE THEORETICAL QUESTION IV
Part MARKING SCHEME - THE THEORETICAL QUESTION IV- COMPTON
SCATTERING
Tota l Sco res
IV. For:
the situation before the first scattering of photon
the momentum pi and the energy E i of the initial photon
⋅
=
⋅
=
=
i i
i i i
f h E
c
f h h P
λ
0.3p
the frequency of initial photon
i i
c f
λ
= 0.1p
the momentum poe and the energy E oe of initial, free electron in motion
−
⋅
=
⋅
=
−
⋅
=
⋅
=
2
2 0 2
2
1 0 1
1
1
β
β
c m c m E
v m v m P
oe
e e
oe
0.3p
De Broglie wavelength of the first electron 2
1 0 0
⋅
⋅
=
=
e e
oe
v m
h p
h
0.2p
the situation after the scattering of photon
7.0 points
Trang 2the momentum p0 and the energy E0 of the scattered photon
⋅
=
⋅
=
=
o o
o o o
f h E
c
f h h P
λ
0.3p
the frequency of scattered photon
0 λ
c
f o = 0.1p
the principles of conservation of moments and energy
+
= +
= +
e e
i
oe i
E E E E
p p P
1 0 0 0
0.3p
the conservation of moment on Ox direction cos α 0 cos θ
1
c
f h v
m c
f h
e
⋅
0.3p
the conservation of moment on Oy sin α 0 sin θ
1
c
f h v
0.3p
1
0
2 1
2 0 2 2 1 2 1
2 2
−
⋅
i e
e
f f f f h v c v
c m
0.4p
The conservation of energy m⋅c2+h⋅f1=m0⋅c2+h⋅f0
0.3p
1
2 0
1
f f h c m c
v
c m
e
−
⋅ +
⋅
=
−
⋅
0.2p
2 1 0 2 4 2 0 2 1
4 2 0
1
f f c h m f f h c m c
v
c m
e
−
⋅
⋅
⋅ +
−
⋅ +
⋅
=
−
⋅
0.2p
0 1 0
cos 1
f
c f
c c
m
h
−
=
−
⋅ θ 0.2p
c m
h
⋅
= Λ
0
0.2p the wavelength of scattered photon λ0 =λi −Λ⋅(1−cosθ ) 0.3p
Trang 3
>
<
0
0
E
E i
λ
0.1p
the situation before the second collision
the situation after this scattering process
The conservation principle for moment in the scattering process
=
⋅
⋅
−
⋅
⋅ +
=
0 sin sin
cos cos
2
2 0
β θ
λ
β θ
λ λ
e f
e f
v m h
v m h
h
0.3p
2 0
2 2
0
2
cos
2
e f
f
v m h
h h
⋅
=
⋅
⋅
−
+
λ λ λ
λ 0.3p
−
⋅Λ
=
−
−
=
−
⋅
⋅
θ λ
λ
λ λ θ
cos 1
cos 1
0
0 0
f
f
c m
h
0.5p
<
>
0
0
E
E f
λ
0.1p
Trang 4
×
=
×
=
×
⋅
×
×
= Λ
×
=
−
−
−
−
m m
m
m
f
10 12
8 31
34
10 02 ,0 10
41
,2 10
3 10 1, 9
10 6, 6
10 25 ,1
λ
0.2p
the value of wavelength of photon before the second scattering 10m
0 =1,23×10−
λ 0.1p
f
i λ
λ =
0.3p
=
=
e e
e e
E E
p p
2 1
2 1
0.2p
the moment of final electron
cos 2 cos
1
1 1
2 2
2
− Λ
−
⋅
⋅
−
− Λ
− +
=
f f f
f
0.4p
The de Broglie wavelength of second electron after scattering (and of first electron before scattering)
− Λ
−
⋅
⋅
−
− Λ
− +
=
=
θ λ
λ
θ θ
λ λ λ
λ
cos 1
cos 2 cos
1
1 1
2 1
f f f
f e
final result: e e 10m
2
1 =λ =1,24×10−
λ 0.2p
nts
Professor Delia DAVIDESCU, National Department of Evaluation and Examination– Ministry of Education and
Research- Bucharest, Romania
Professor Adrian S.DAFINEI,PhD, Faculty of Physics University of Bucharest, Romania–