Question

In Compton scattering, the incoming and scattered photons have a different wavelength. If the outgoing photon has a wavelength which is 12% more than the incoming, what is the ratio of the outgoing photon energy to the incoming photon energy (E subscript text out end text end subscript over E subscript text in end text end subscript)? (2 s.f.)

Answer 1

Given

Wavelength of outgoing photon is $\lambda _{out}=(0.12+1)\lambda _{in}=1.12 \lambda _{in}$

The ratio of the outgoing photon energy to the incoming photon energy is

$\frac{E_{out}}{E_{in}}=\frac{\frac{hc}{\lambda _{out}}}{\frac{hc}{\lambda _{in}}}$

$\frac{E_{out}}{E_{in}}=\frac{\lambda _{in}}{\lambda _{out}}$

$=\frac{\lambda _{in}}{1.12\lambda _{in}}$

$=\frac{1}{1.12}=0.89$

Hence, the ratio of the outgoing photon energy to the incoming photon energy is$\frac{E_{out}}{E_{in}}=\frac{1}{1.12}=0.89$ .