A photon whose energy equals the rest energy of the electron undergoes Compton collision with an electron. if the electron moves off at an angle of 40 degree with the original photon Direction What is the energy of the scattered photon?
Answers
Answer:
Unlike a particle of matter that is characterized by its rest mass {m}_{0}, a photon is massless. In a vacuum, unlike a particle of matter that may vary its speed but cannot reach the speed of light, a photon travels at only one speed, which is exactly the speed of light.According to the theory of special relativity, any particle in nature obeys the relativistic energy equation
{E}^{2}={p}^{2}{c}^{2}+{m}_{0}^{2}{c}^{4}.
This relation can also be applied to a photon. For a photon, we simply set {m}_{0}=0 in this equation.
{p}_{f}=\frac{{E}_{f}}{c}.
Here the photon’s energy {E}_{f} is the same as that of a light quantum of frequency f, which we introduced to explain the photoelectric effect:
{E}_{f}=hf=\frac{hc}{\lambda }.
The wave relation that connects frequency f with wavelength \lambda and speed c also holds for photons:
\lambda f=c
Therefore, a photon can be equivalently characterized by either its energy and wavelength, or its frequency and momentum and can be combined into the explicit relation between a photon’s momentum and its wavelength:
{p}_{f}=\frac{h}{\lambda }.
Explanation: