Question

In Compton scattering a photon collides with an electron that is initially at rest.

(a) Rank the following quantities in order from largest to smallest. If any two quantities are the same, state this. Explain how you made your ranking.

(i) The wavelength of an x-ray photon

(ii) The change in wavelength of an x-ray photon in Compton scattering when it scatters through an angle of 0° (that is, the photon continues in the same direction as its initial motion)

(iii) The change in wavelength of an x-ray photon in Compton scattering when it scatters through an angle of 90° (that is, the photon is scattered in a direction at right angles to its initial motion)

(iv) The change in wavelength of an x-ray photon in Compton scattering when it scatters through an angle of 180° (that is, the photon is scattered in the direction opposite to its initial motion)

(b) Fill in the blanks in each of the following statements with the word increases, the word decreases, the phrase stays the same, or the phrase don’t know.

(i) In Compton scattering if the angle through which the photon is scattered increases, the energy of the scattered photon ____________, the momentum of the scattered photon __________, the frequency of the scattered photon __________, and the speed of the scattered photon __________.

(ii) In Compton scattering if the angle through which the photon is scattered increases, the kinetic energy of the scattered electron __________, the momentum of the scattered electron __________, and the speed of the scattered electron __________.

Answer 1

(a) In a compton experiment the wavelength of the scattered photon is given by the expression:${\lambda }'=\lambda _{0}+\frac{h}{mc}(1-\cos \theta )$

So we can see that if the angle is 0° the wavelength of the incident photon does not change (in other words, the change in wavelength is zero), if it's 90° then it's larger by the amount h/mc (this is known as the compton wavelength and it's approximately equal to 2.4pm) and if it's 180° (backscattering) it increases by two times the compton wavelength. Therefore the rank from largest to smallest would be

(b)

(i) In Compton scattering if the angle through which the photon is scattered increases, the energy of the scattered photon decreases, the momentum of the scattered photon decreases, the frequency of the scattered photon decreases, and the speed of the scattered photon stays the same.

(ii) In Compton scattering if the angle through which the photon is scattered increases, the kinetic energy of the scattered electron increases, the momentum of the scattered electron increases, and the speed of the scattered electron increases.