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Q. The $K_{a}$ line from molybdenum (atomic number $=42$ ) has a wavelength of $0.7078\, \mathring{A}$. The wavelength of $K_{a}$ line of zinc (atomic number $=30$ ) will be

AIIMSAIIMS 2011

Solution:

Wavelength $\lambda=0.7078 \, \mathring{A}$
Energy$E=\frac{h c}{\lambda}$
$\frac{z^{2}}{n^{2}}=\frac{h c}{\lambda}$
$\therefore \quad \frac{z_{1}^{2}}{z_{2}^{2}}=\frac{\lambda_{2}}{\lambda_{1}}$
$\frac{(42)^{2}}{(30)^{2}}=\frac{\lambda_{2}}{0.7078}$
$\lambda=1.3873 \, \mathring{A}$