Question

The Balmer series in the hydrogen spectrum corresponds to the transition from $n_{1=2}$ to $n_{2=3,4,.....}$ This series lies in the visible region. Calculate the wave number of line associated with the transition in Balmer series when the electron moves to $n=4$ orbit. $(R_H=109677c{m}^{-1})$

Answer 1

Here $n_1=2,n_2=4$
$\overline{v}=109677[\frac{1}{n_1^2}-\frac{1}{n_2^2}]c{m}^{-1}$
for $n_1=2,n_2=4$ transition in Balmer series.
$\overline{v}=109677[\frac{1}{2^2}-\frac{1}{4^2}]$
$=109677[\frac{1}{4}-\frac{1}{16}]=20564.44c{m}^{-1}$