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 $n_{i}=3,4,5, \ldots$
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
$\frac{f}{f^{\prime}}=\frac{20}{27}$
$\therefore f^{\prime}=\frac{27}{20} f=1.35 f$