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Using Rydberg Formula, Calculate the Wavelengths of the Spectral Lines of the First Member of the Lyman Series and of the Balmer Series. - Physics

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ConceptHydrogen Spectrum

Question

Using Rydberg formula, calculate the wavelengths of the spectral lines of the first member of the Lyman series and of the Balmer series.

Solution

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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Solution Using Rydberg Formula, Calculate the Wavelengths of the Spectral Lines of the First Member of the Lyman Series and of the Balmer Series. Concept: Hydrogen Spectrum.
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