Question

The wavelength of $K_{\alpha}$ line for an element of atomic number $29$ is $\lambda$. The wavelength of $K_{\alpha}$ line for an element of atomic number $15$ is $\beta \lambda$. Find $\beta$. (Take Moseley's constant, $b=1$ for both elements)

Answer 1

$\frac{1}{\lambda} \propto(Z-b)^{2}$;
$ \frac{\lambda_{2}}{\lambda_{1}}=\frac{\left(Z_{1}-b\right)}{\left(Z_{2}-b\right)}=\left(\frac{28}{14}\right)^{2}=4$
$\lambda_{2}=4 \lambda_{1}=4 \lambda$