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  4. The wavelength of the third line of the Balmer series for a hydrogen atom is

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Q. The wavelength of the third line of the Balmer series for a hydrogen atom is

NTA AbhyasNTA Abhyas 2020Structure of Atom

Solution:

$\frac{1}{\lambda }=R_{H}\left(\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}\right)$ for the H-atom

For the Balmer series,

$n_{1}=2$ and $n_{2}=5$ (for the third line).

$\frac{1}{\lambda }=R_{H}\left(\frac{1}{2^{2}} - \frac{1}{5^{2}}\right)=\frac{21}{100}R_{H}$

So $\lambda \, \text{=} \, \frac{\text{100}}{\text{21R}_{H}}$