Question

If the wave number of first line of Balmer series of $H$-atom is ' $x$ ' then the wave number of first line of Lyman series of the $He ^{+}$ion will be expressed as $Z \times x$. Find the value of $Z$?

Answer 1

$\overline{ V }=R Z^{2}\left(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right)$
$x=R\left(\frac{1}{2^{2}}-\frac{1}{3^{2}}\right)=\frac{5 R}{36}$
$\bar{v}_{1}=R \times 2^{2}\left(1-\frac{1}{2^{2}}\right)=3 R$
$=\frac{36}{5} x \times 3=\frac{108 x}{5}$