Number 48 on page 938 of Cutnell and Johnson Physics 7thedition: In the compton

Question

Number 48 on page 938 of Cutnell and Johnson Physics 7thedition:

In the compton effect, momentum conservation applies, so the totalmomentum of the photon and the electron is the same before andafter the scattering occurs. Suppose in figure 29.10 that thedirection of the incident photon is in the +x direction and thatthe scattered photon emerges at an angle of =90, which is inthe -y direction.
(a) Before the scattering, the total momentum has an x component.Does it have a y component?
(b) After the scattering, the total momentum has an x component.Does it have a y component?
(c) Does the momentum of the scattered electron have an xcomponent?
(d) Considering your answer to question (b) and considering thefact that the scattered photon is moving along the -y axis, doesthe momentum of the scattered electron have a y component?

Justify your answers.

Explanation / Answer

(a)    before the scattering, the electron is atrest and has no momentum. Thus, the total initial momentumconsists only of the    photon momentum, which points along the+x axis. The total initial momentum has no ycomponent. (b)    since the total momentum is conserved, thetotal momentum after the scattering must be the same as it wasbefore and,    therefore, has no ycomponent. (c)    the total momentum after the scattering isthe sum of the momentum of the scattered photon and that of thescattered    electron, and it has an xcomponent. But the scattered photon is moving along the–y axis, so its momentum has no x    component. Therefore, the momentum ofthe electron must have an x component. (d)    the total momentum after the scattering isthe sum of the momentum of the scattered photon and that of thescattered
   electron, and it has no ycomponent. But the scattered photon is moving along the–y axis, so its momentum points along
   the –y axis. Therefore, thiscontribution to the total final momentum must be cancelled by partof the momentum of the
   scattered electron, which must have a componentalong the +y axis

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