Question

Assuming $f$ to be the frequency of first line in Balmer series, the frequency of the immediate next (i.e. second) line is Assuming $f$ to be the frequency of first line in Balmer series, the frequency of the immediate next (i.e. second) line is

• A. 0.50 f
• B. 1.35 f
• C. 2.05 f
• D. 2.70 f

Answer 1

Answer: (B)

Balmer series is the series in which the spectral lines correspond to the transition of electron from some higher energy state to the lower energy state corresponding to $n_f=2$. Therefore, for Balmer series, $n_f=2$ and $n_i=3,4,5,\dots$
Frequency, of 1 st spectral line of Balmer
series $f=R{Z}^{2}c\left(\frac{1}{2^2}-\frac{1}{3^2}\right)$
Or $f=R{Z}^{2}c\times \frac{5}{36}....$(i)
Frequency of 2 nd spectral line of Balmer series
$f^{\prime }=R{Z}^{2}c\left(\frac{1}{2^2}-\frac{1}{4^2}\right)$
or $f^{\prime }=R{Z}^{2}c\times \frac{3}{16}....$(ii)
From Eqs. (i) and (ii), we have
$\frac{f}{f^{\prime }}=\frac{20}{27}$
$\therefore f^{\prime }=\frac{27}{20}f=1.35f$