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Q.
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
NTA AbhyasNTA Abhyas 2022
Solution:
For Balmer series, $n_{f}$ =2 and $n_{i}$ =3,4,5,....
Frequency, of 1st spectral line of Balmer series
$ \, \, \, f$ $=$ $RZ^{2} \, c\left(\frac{1}{2^{2}} - \frac{1}{3^{2}}\right)$
or $ \, \, \, f=RZ^{2} \, c\times \frac{5}{36}$ ...(i)
Frequency, of 2nd spectral line of Balmer series
$ \, \, f’ \, =$ $RZ^{2} \, c\left(\frac{1}{2^{2}} - \frac{1}{4^{2}}\right)$
or $ \, \, f′=RZ^{2} \, c\times \frac{3}{16}$ ....(ii)
Form eqs. (i) and (ii), we have
$ \, \frac{f}{f ′}$ $=\frac{20}{27}$
$\therefore \, \, f^{′}=\frac{27}{20} \, f=1.35 \, f$