First slide

Hydrogen spectrum

Question

If R is the Rydberg constant for hydrogen, then the wave number of the first line in the Lyman series is

Moderate

A

$\frac{R}{2}$
B

$2 R$
C

$\frac{R}{4}$
D

$\frac{3 R}{4}$

Solution

$\frac{1}{λ} = R [\frac{1}{1^{2}} - \frac{1}{2^{2}}]$
$or \frac{1}{λ} = R [1 - \frac{1}{4}] = \frac{3 R}{4}$
Hence, wavenumber
$\frac{1}{λ} = \frac{3 R}{4}$

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