Explanation

(c) The wavelength of $X$-ray lines is given by Rydberg
$Formula\frac{1}{\lambda} = RZ^{2}\left( \frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}} \right)$
For $K_{\alpha}$ line, $n_{1} = 1$ and $n_{2} = 2$
$\therefore\frac{1}{\lambda} = RZ^{2}\left( \frac{3}{4} \right) \Rightarrow Z = \left( \frac{4}{3R\lambda} \right)^{1/2}$
$= \left\lbrack \frac{4}{3\left( 1.097 \times 10^{7}m^{- 1} \right)\left( 0.76 \times 10^{- 10}m \right)} \right\rbrack^{1/2} = 39.99 \approx 40$