Question

In a Compton-shift experiment, light (in the x-ray range) is scattered in the forward direction, at$\mathit{\varphi }\mathbf{=}\mathbf{0}$ in Fig. 38-3. What fraction of the light’s energy does the electron acquire?

Short answer

None of the fraction of light’s energy is acquired by the electron.

Step-by-step solution

Describe the change in wavelength in Compton Effect

The change in wavelength in Compton Effect is given by,

$\mathit{\Delta }\mathit{\lambda }\mathbf{=}\frac{\mathbf{h}}{\mathbf{m}\mathbf{c}}\left(1-cos\varphi \right)$

Here,role="math" localid="1663133543883" $\mathit{\Delta }\mathit{\lambda }$ is the Compton shift, h is the Planck’s constant, m is the mass of the electron, c is the speed of light, and$\mathit{\varphi }$ is the scattering angle.

Find the fraction of the light’s energy does the electron acquire

Consider the following equation.

$\Delta \lambda =\frac{h}{mc}\left(1-\cos \varphi \right)$

Here,$\varphi =0$

$$\begin{gathered} \Delta \lambda =\frac{h}{mc}\left(1-\cos 0\right) \\ =\frac{h}{mc}\left(1-1\right) \\ =0 \end{gathered}$$

As $\Delta \lambda =0$, therefore, the change in wavelength is zero. So, there is no energy transferred to the electron.

Therefore, none of the fraction of light’s energy is acquired by the electron.