Serway Problem $27\mathrm{.}26-$ the Compton effect:

A $25\mathrm{.}0-$pm x$-$ray photon scatters off a free electron at $A($Fig$.$ P$27\mathrm{.}26),$ producing a photon of wavelength $i^{\text{'}}$ traveling at an angle $=40\mathrm{.}0$ relative to the first photon's direction. This second photon scatters off another free electron at $B,$ producing a photon with wavelength ${}^{\text{'}}$ and moving in a direction directly opposite the first photon. Determine the wavelengths

a$.i^{\text{'}}$ and

b$.{}^{\text{'}\text{'}}.$

Figure P$27\mathrm{.}26$

Details

An illustration shows a photon colliding with an electron at position A$.$ The scattered photon after collision at position A collides with another electron at position B$.$ A photon of wavelength lambda is incident on the first electron at the position A $,$ and gets scattered downward with wavelength lambda prime, at an angle of theta with respect to the direction of incident photon. The electron at A$,$ after collision gains energy and moves upward at an angle of alpha with respect to the direction of incident photon, and is labeled electron $1.$ The scattered photon strikes the second electron at the position B and gets scattered at the direction opposite to the incident photon with wavelength lambda double prime. After collision, the second electron at B$,$ gains energy and moves downward making angle beta with respect to the scattered photon of wavelength lambda prime, and is labeled electron $2.$