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  4. The ratio of the longest to the shortest wavelengths in the Brackett series of hydrogen spectra is:

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Q. The ratio of the longest to the shortest wavelengths in the Brackett series of hydrogen spectra is:

NTA AbhyasNTA Abhyas 2022

Solution:

For the Brackett series, $\frac{1}{\lambda _{max}}=R\left[\frac{1}{4^{2}} - \frac{1}{5^{2}}\right]=\frac{9}{25 \times 16}R$
and
$\frac{1}{\lambda _{min}}=R\left[\frac{1}{4^{2}} - \frac{1}{\infty ^{2}}\right]=\frac{R}{16}$
Therefore, $\frac{\lambda _{max}}{\lambda _{min}}=\frac{25}{9}$