2. The Compton effect involves the collision of a photon and a stationary, free electron, as shown in the figure. The electron often re- coils at relativistic speeds, and photons al- ways travel at relativistic speed. So we must use the relativistic relationship for mass, mo- mentum, and energy: 2 2 2 E₂² = c²p₂²+ m₂ ²c4 E = c = Esp E+m₂c² = E' + E₂ p=p'cos+p₂ cos 0=p'sine - pesino (1) In class we showed that conservation of energy and momentum in the collision yield the following three equations: hc E',p' hc E' = cp' = 2 (a) Combine equations (1)-(4) and the relations between photon energy, momentum and wavelength, tano = 0 (b) Show that the electron scattering angle, o, is given by: E' sine E-E' cose o and to obtain the Compton equation, relating the photon wavelength shift (2′ − 2) and the photon scattering angle (0): Ees Pe " (2) (3) (4) h 2-λ=- -(1-cose). mec [Hint: First eliminate the angle from the equations and express på in terms of p, p' and 0, by using equations (3) and (4) and cos² (p) + sin²(p) = 1.]
2. The Compton effect involves the collision of a photon and a stationary, free electron, as shown in the figure. The electron often re- coils at relativistic speeds, and photons al- ways travel at relativistic speed. So we must use the relativistic relationship for mass, mo- mentum, and energy: 2 2 2 E₂² = c²p₂²+ m₂ ²c4 E = c = Esp E+m₂c² = E' + E₂ p=p'cos+p₂ cos 0=p'sine - pesino (1) In class we showed that conservation of energy and momentum in the collision yield the following three equations: hc E',p' hc E' = cp' = 2 (a) Combine equations (1)-(4) and the relations between photon energy, momentum and wavelength, tano = 0 (b) Show that the electron scattering angle, o, is given by: E' sine E-E' cose o and to obtain the Compton equation, relating the photon wavelength shift (2′ − 2) and the photon scattering angle (0): Ees Pe " (2) (3) (4) h 2-λ=- -(1-cose). mec [Hint: First eliminate the angle from the equations and express på in terms of p, p' and 0, by using equations (3) and (4) and cos² (p) + sin²(p) = 1.]
Related questions
Question
![2. The Compton effect involves the collision of
a photon and a stationary, free electron, as
shown in the figure. The electron often re-
coils at relativistic speeds, and photons al-
ways travel at relativistic speed. So we must
use the relativistic relationship for mass, mo-
mentum, and energy:
E, p
2
2
E₂² = c²p₂² + m₂ ²c²
E+m₂c² = E' + E₂
p=p'cose+p₂ cos
0= p'sine pe sino
E', p
(1)
In class we showed that conservation of energy and momentum in the collision yield
the following three equations:
(2)
Ø
Ees Pe
(b) Show that the electron scattering angle, o, is given by:
E' sin 0
E- E' cose
tano =
(a) Combine equations (1)-(4) and the relations between photon energy, momentum
and wavelength,
(4)
hc
E = cp =
and
E' = cp' = hc
λ
to obtain the Compton equation, relating the photon wavelength shift (2' - 2) and
the photon scattering angle (0):
h
2²-2=- -(1-cose).
mec
[Hint: First eliminate the angle & from the equations and express p² in terms of p,
p' and 0, by using equations (3) and (4) and cos² (p) + sin²(p) = 1.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29c74d06-0f3b-4eb2-9c9d-dbbc1918002c%2F144c32d4-273e-46b8-a197-233e0e459264%2Fdr76vfk_processed.png&w=3840&q=75)
Transcribed Image Text:2. The Compton effect involves the collision of
a photon and a stationary, free electron, as
shown in the figure. The electron often re-
coils at relativistic speeds, and photons al-
ways travel at relativistic speed. So we must
use the relativistic relationship for mass, mo-
mentum, and energy:
E, p
2
2
E₂² = c²p₂² + m₂ ²c²
E+m₂c² = E' + E₂
p=p'cose+p₂ cos
0= p'sine pe sino
E', p
(1)
In class we showed that conservation of energy and momentum in the collision yield
the following three equations:
(2)
Ø
Ees Pe
(b) Show that the electron scattering angle, o, is given by:
E' sin 0
E- E' cose
tano =
(a) Combine equations (1)-(4) and the relations between photon energy, momentum
and wavelength,
(4)
hc
E = cp =
and
E' = cp' = hc
λ
to obtain the Compton equation, relating the photon wavelength shift (2' - 2) and
the photon scattering angle (0):
h
2²-2=- -(1-cose).
mec
[Hint: First eliminate the angle & from the equations and express p² in terms of p,
p' and 0, by using equations (3) and (4) and cos² (p) + sin²(p) = 1.]
Expert Solution
Step 1
Compton effect:
When a photon of a particular wavelength is made to collide with an electron at rest, then after the collision, the wavelength of the photon is increased. This is called the Compton effect.
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