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  4. In Brackett series of hydrogen spectra, what is the ratio of the longest to shortest wavelengths?

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Q. In Brackett series of hydrogen spectra, what is the ratio of the longest to shortest wavelengths?

NTA AbhyasNTA Abhyas 2020

Solution:

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