First slide

Hydrogen spectrum

Question

If the series limit wavelength of the Lyman series for hydrogen atom is 912 $Å$ , then the series limit wavelength for the Balmer series for the hydrogen atom is

Moderate

A

$912 Å / 2$
B

$912 Å$
C

$912 \times 2 Å$
D

$912 \times 4 Å$

Solution

For Lyman series, the series limit wavelength is given by
$\frac{1}{λ} = R [\frac{1}{1^{2}} - \frac{1}{\infty^{2}}] = R or λ = \frac{1}{R}$
For Balmer series, the series limit wavelength is given by
$\frac{1}{λ^{'}} = R [\frac{1}{2^{2}} - \frac{1}{\infty^{2}}] = \frac{R}{4} or λ^{'} = \frac{4}{R}$
Clearly,
$λ^{'} = 4 [\frac{1}{R}] or λ^{'} = 4 λ = 4 \times 912 Å$

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