Question

Compton scattering. Figure 38-22 gives the Compton shift versus scattering angle$\mathit{\varphi }$ for three different stationary target particles. Rank the particles according to their mass, greatest first.

Short answer

The rank of the particles according to their mass is 3, 2, 1.

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, $\mathit{\Delta }\mathit{\lambda }$is 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.

Rank the particles according to their mass, greatest first

Consider the following equation.

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

From the above equation, it can be clearly observed that the change in wavelength is inversely proportional to the mass of the particle.

From the given diagram, it can be observed that the wavelength is maximum for 1 and least for 3.

Therefore, the rank of the particles according to their mass is 3, 2, 1.