SATHEE: atoms Question 21

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Question: Q. 15. The short wavelength limit for the Lyman series of the hydrogen is $913.4 \AA$ . Calculate the short wavelength limit for Balmer series of hydrogen spectrum.

A [CBSE SQP 2014]

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Solution:

Ans. Rydberg formula for the wavelengths of spectral lines in hydrogen spectrum is

$\frac{1}{λ} = R (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}})$

The short wavelength limit $λ_{L}$ for the Lyman series would be

$\begin{aligned} \frac{1}{λ_{L}} & = R (\frac{1}{1^{2}} - \frac{1}{\infty^{2}}) = R & ∴ & R & = \frac{1}{913.4 \AA} \end{aligned}$

$∴$ The short wavelength limit $λ_{B}$ for the Balmer series, would be

$\begin{aligned} \frac{1}{λ_{B}} & = R (\frac{1}{2^{2}} - \frac{1}{\infty^{2}}) = \frac{R}{4} ∴ λ_{B} & = \frac{4}{R} = 4 \times 913.4 \AA & = 3653.6 \AA \end{aligned}$

[CBSE Marking Scheme 2014]

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