Question

The wavelength of the $K_{a}$ line for an element of atomic number $57$ is $\alpha$. The wavelength of the $K_{a}$ line for the element of atomic number $29$ is $b \alpha$. Find $b$.

Answer 1

$E=(10.2 \,eV )(Z-1)^{2}$
$\frac{h c}{\lambda}=(10.2\, eV )(Z-1)^{2}$
$\frac{\lambda_{2}}{\lambda_{1}}=\frac{\left(Z_{1}-1\right)^{2}}{\left(Z_{2}-1\right)^{2}}$ ;
$ \frac{\lambda_{2}}{\alpha}=\frac{(56)^{2}}{(28)^{2}} $
$\Rightarrow \lambda_{2}=4 \alpha$