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Q.
The frequency of the first line of Balmer series in hydrogen atom is $v_{0}\, Hz$. The frequency $v$ of this line emitted by a singly ionized He-atom is
Atoms
Solution:
$v=Z^{2} R c\left[\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right]$
For hydrogen atom,
$v_{0}=(1)^{2} R c\left[\frac{1}{2^{2}}-\frac{1}{3^{2}}\right]=\frac{5 R c}{36}$
For singly ionised He atom,
$ v=(2)^{2} R c\left[\frac{1}{2^{2}}-\frac{1}{3^{2}}\right]=\frac{20\, R c}{36} $
$\therefore \frac{v}{v_{0}}=4 \text { or } v=4 v_{0}$