Q. The intensity distribution of $X$-rays from two coolidge tubes operated on different voltages $V_{1}$ and $V_{2}$ and using different target materials of atomic numbers $Z_{1}$ and $Z_{2}$ is shown in the figure. Which one of the following inequalities is true
A) $V_{1} > V_{2},Z_{1} < Z_{2}$
B) $V_{1} > V_{2},Z_{1} > Z_{2}$
C) $V_{1} < V_{2},Z_{1} > Z_{2}$
D) $V_{1} = V_{2},Z_{1} < Z_{2}$
Explanation
(a) $\lambda_{\min} = \frac{hc}{eV} \Rightarrow \lambda \propto \frac{1}{V}$
$\because\lambda_{2} > \lambda_{1}$ (see graph) $\Rightarrow V_{1} > V_{2}$
$\sqrt{v} = a(Z - b)\ $Moseley's law
$v \propto (Z - 1)^{2} \Rightarrow \lambda \propto \frac{1}{(Z - 1)^{2}}\ \ \ \ \left\lbrack \because v \propto \frac{1}{\lambda} \right\rbrack$
$\lambda_{1} > \lambda_{2}$ [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.