First slide

Hydrogen spectrum

Question

The first line in the Lyman series has wavelength $λ$ . The wavelength of the first line in Balmer series is

Easy

A

$\frac{2}{9} λ$
B

$\frac{9}{2} λ$
C

$\frac{5}{27} λ$
D

$\frac{27}{5} λ$

Solution

For first line in Lyman series $λ_{L_{1}} = \frac{4}{3 R}$ …….(i)
For first line in Balmer series, $λ_{B_{1}} = \frac{36}{5 R}$ ……(ii)
From equations (i) and (ii),
$\frac{λ_{B_{1}}}{λ_{L_{1}}} = \frac{27}{5} \Rightarrow λ_{B_{1}} = \frac{27}{5} λ_{L_{1}} Thus, λ_{B_{1}} = \frac{27}{5} λ$

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