First slide

Bohr Model of the Hydrogen atom.

Question

The wavelengths of the first line in Balmer series in hydrogen spectrum is $λ$ What is the wavelength of second line

Easy

A

$\frac{20}{27} λ$
B

$\frac{27}{20} λ$
C

$\frac{5}{36} λ$
D

$\frac{36}{5} λ$

Solution

For first line of Balmer series, we have
$\frac{1}{λ_{1}} = R [\frac{1}{4} - \frac{1}{9}] = \frac{5 R}{36} For second line of Balmer series \frac{1}{λ_{2}} = R [\frac{1}{4} - \frac{1}{16}] = \frac{3 R}{16} \frac{λ_{2}}{λ_{1}} = \frac{16 \times 5}{3 \times 36} = \frac{20}{27} or λ_{2} = \frac{20}{27} λ$

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