Q.
When two different materials A and B having atomic number $Z_{1}$ and $Z_{2}$ are used as the target in Coolidge $\gamma$-ray tube at different operating voltage $V_{1}$ and $V_{2}$ respectively their spectrums are found as below.
The correct relation is
A) $V_{1} > V_{2}$ and ${\ Z}_{1} > Z_{2}$
B) $V_{1} < V_{2}$ and $Z_{1} < Z_{2}$
C) $V_{1} < V_{2}$ and $Z_{1} > Z_{2}$
D) $V_{1} > V_{2}$ and $Z_{1} < Z_{2}$
Explanation
(d) ${\lambda\ }_{\min} = \frac{hc}{eV}$
$\Rightarrow \ \ \ \ \ \ \ \lambda \propto \frac{1}{V}$
$\because\ \ \ \ \ \ \ \ \lambda_{2} > \ \lambda_{1}$ (see graph)
$\Rightarrow \ \ \ \ V_{1} > V_{2}$
$\sqrt{v} = a(Z - b)$ Moseley’s law
$\ v$ $\propto (Z - 1)^{2}$
$\Rightarrow \ \ \ \lambda\ \propto \frac{1}{(Z - 1)^{2}}$ ($\because v \propto \frac{1}{\lambda})$
$\ \ \lambda_{1} > \ \lambda_{2}$ (see graph for characteristic lines)
$\Rightarrow \ \ \ \ \ \ Z_{2} > \ $ $Z_{1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.