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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

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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