What is the shortest wavelength present in the Paschen series of spectral lines?

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What is the shortest wavelength present in the Paschen series of spectral lines?

What is the shortest wavelength present in the Paschen series of spectral lines?

Answer –

Using the Rydberg’s formula, given the relation –

$\frac{hc}{\lambda }=21.76\times {{10}^{-19}}[\frac{1}{{{n}_{1}}^{2}}-\frac{1}{{{n}_{2}}^{2}}]$

Where

h is the Planck’s constant, given = 6.6 × 10^-34

c is the speed of the light, given = 3 × 10⁸ m/s

and n₁ and n₂ are integers.

We know that in the Paschen series of the spectral lines, the shortest wavelength corresponds for the following values –

n₁ = 3 and n₂ = ∞, from above formula we get –

$\frac{hc}{\lambda }=21.76\times {{10}^{-19}}[\frac{1}{{{3}^{2}}}-\frac{1}{{{\infty }^{2}}}]$

$\lambda =\frac{9}{8\times 1.097\times {{10}^{7}}}=102.55nm$

$\lambda =\frac{6.6\times {{10}^{-34}}\times 3\times {{10}^{8}}\times 9}{21.76\times {{10}^{-19}}}\text{= }8.189~\times \text{ }{{10}^{7}}~m$

$\therefore \lambda =818.9nm$

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