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  4. When R is Rydbergs constant for hydrogen, the wave number of the first line in the Lyman series is:

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Q. When R is Rydbergs constant for hydrogen, the wave number of the first line in the Lyman series is:

Bihar CECEBihar CECE 2001Atoms

Solution:

When an electron in an atom jumps from higher orbits to the ground orbit, Lyman series is found. The wavelength of lines obtained in Lyman series is given by
$ \frac{1}{\lambda }=R\left( \frac{1}{{{1}^{2}}}-\frac{1}{{{n}^{2}}} \right) n=2,3,4,..... $
For first line of Lyman series, $ n=2 $
$ \therefore $ $ \bar{v}=\frac{1}{{{\lambda }_{1}}}=R\left( \frac{1}{{{1}^{2}}}-\frac{1}{{{2}^{2}}} \right) $
or $ =R\left( \frac{4-1}{4} \right) $
or $ \bar{v}=\frac{3R}{4} $
Note: For shortest wavelength of Lyman series, put $ n=\infty . $