Answer
$m_{3}\gt m_{2}\gt m_{1}$
Work Step by Step
The Compton shift $\Delta\lambda$ is given by the formula:
$\Delta\lambda=\frac{h}{mc}(1-\cos\phi)$
Now for constant scattering angle $\phi$,
$\Delta\lambda \propto \frac{1}{m}$,
where $m$ is the mass of stationary target particle.
According to the figure 38-22, at a constant $\phi$,
$\Delta\lambda^1\gt \Delta\lambda^2\gt \Delta\lambda^3$
or, $\frac{1}{m_{1}}\gt \frac{1}{m_{2}}\gt \frac{1}{m_{3}}$
or, $m_{1}\lt m_{2}\lt m_{3}$
or, $m_{3}\gt m_{2}\gt m_{1}$
where $ m_{1}$, $m_{2}$ and $m_{3}$ are the masses of target particle 1, 2 and 3 respectively.
Thus, the rank of particles according their mass is $m_{3}\gt m_{2}\gt m_{1}$
