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प्रश्न
Using Rydberg formula, calculate the wavelengths of the spectral lines of the first member of the Lyman series and of the Balmer series.
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उत्तर
The Rydberg formula for the spectrum of the hydrogen atom is given below:
\[\frac{1}{\lambda} = R\left[ \frac{1}{{n_1}^2} - \frac{1}{{n_2}^2} \right]\]
Here,
\[\lambda\] is the wavelength and R is the Rydberg constant.
R = \[1 . 097 \times {10}^7\] m-1
For the first member of the Lyman series:
\[n_1 = 1 \]
\[ n_2 = 2\]
Now,
\[\frac{1}{\lambda} = 1 . 097 \times {10}^7 \left[ \frac{1}{1^2} - \frac{1}{2^2} \right]\]
\[\Rightarrow \lambda = 1215 A^o\]
For the first member of the Balmer series:
\[n_1 = 2 \]
\[ n_2 = 3\]
Now,
\[\frac{1}{\lambda} = 1 . 097 \times {10}^7 \left[ \frac{1}{2^2} - \frac{1}{3^2} \right]\]
\[\Rightarrow \lambda = 6563 A^o\]
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