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An x-ray photon is scattered from a free electron (mass m)
Chapter 38, Problem 42P(choose chapter or problem)
Problem 42P
An x-ray photon is scattered from a free electron (mass m) at rest. The wavelength of the scattered photon is λ’, and the final speed of the struck electron is v. (a) What was the initial wavelength λ of the photon? Express your answer in terms of λ’, v, and m. (Hint: Use the relativistic expression for the electron kinetic energy.) (b) Through what angle Φ is the photon scattered? Express your answer in terms of λ, λ’, and m. (c) Evaluate your results in parts (a) and (b) for a wavelength of 5.10 × 10-3 nm for the scattered photon and a final electron speed of 1.80 × 108 m/s. Give Φ in degrees.
Questions & Answers
QUESTION:
Problem 42P
An x-ray photon is scattered from a free electron (mass m) at rest. The wavelength of the scattered photon is λ’, and the final speed of the struck electron is v. (a) What was the initial wavelength λ of the photon? Express your answer in terms of λ’, v, and m. (Hint: Use the relativistic expression for the electron kinetic energy.) (b) Through what angle Φ is the photon scattered? Express your answer in terms of λ, λ’, and m. (c) Evaluate your results in parts (a) and (b) for a wavelength of 5.10 × 10-3 nm for the scattered photon and a final electron speed of 1.80 × 108 m/s. Give Φ in degrees.
ANSWER:
Introduction
We have to first find out initial wavelength of the light using final wavelength , velocity of electron
and mass of electron
. Then we have to find out the relationship of scattering angle
, with
,
and
. Then we have to calculate the initial wavelength and scattering angle for the given values.
Step 1
(a) We have to conservation of energy to calculate the initial wavelength.
If the initial wavelength is , then the initial energy is given by
And the final kinetic energy of the photon is
And the kinetic energy of the electron is
Where
Now using the conservation of energy we can write that
