Q. If $f_{1},f_{2}$ and $f_{3}$ are the frequencies of corresponding $K_{\alpha},K_{\beta}$ and $L_{\alpha}X$-rays of an element, then
A) $f_{1} = f_{2} = f_{3}$
B) $f_{1} - f_{2} = f_{3}$
C) $f_{2} = f_{1} + f_{3}$
D) $f_{2}^{2} = f_{1}f_{3}$
Explanation
(c) For $k_{\alpha}$ emission
transition $L$ shell to $k -$ shell
For $k_{\beta}$ emission
transition $M$ shell to $k -$ shell
For $L_{\alpha}$ emission
transition $M$ shell to $L -$ shell
$E_{M} - E_{K} = \left( E_{M} - E_{L} \right) + (E_{L} - E_{K})$
$\Rightarrow hf_{2} = hf_{3} + hf_{1} \Rightarrow f_{2} = f_{1} + f_{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.