Question

If the lowest energy $x$ -rays have $\lambda=4.0 \times 10^{-8} m ,$ at what $z$ (minimum) would a transition from the second energy level to the first result in the emission of X-ray?

Answer 1

$\lambda=4 \times 10^{-8} m =400 \,\mathring{A}$,

energy of photon $=\frac{12375}{\lambda}\, eV$

So ; $\frac{12375}{400}=13.6 Z ^{2}\left(1-\frac{1}{4}\right)$

$\Rightarrow Z^{2}=3.04$

$\Rightarrow Z=1.74 \sim 2$ (Helium)