Question

Assuming $f$ to be the frequency of the electromagnetic wave corresponding to the first line in Balmer series, the frequency of the immediate next line is

• A. $0.5f$
• B. $1.35f$
• C. $2.05f$
• D. $2.70f$

Answer 1

Answer: (B)

For Balmer series, $n_f$ =2 and $n_i$ =3,4,5,....
Frequency, of 1st 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 2nd spectral line of Balmer series
$f’=$ $R{Z}^{2}c\left(\frac{1}{2^2}-\frac{1}{4^2}\right)$
or $f\prime =R{Z}^{2}c\times \frac{3}{16}$ ....(ii)
Form eqs. (i) and (ii), we have
$\frac{f}{f\prime }$ $=\frac{20}{27}$
$\therefore f^{\prime }=\frac{27}{20}f=1.35f$