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Question

If λ₁ and λ₂ are the wavelengths of the first members of the Lyman and Paschen series respectively, then λ₁ : λ₂ is

1:3

1: 30

7: 50

7: 108

Solution

7: 108

For first line of Lyman series,

$n_{1} = 1 and n_{2} = 2$

∴ $\frac{1}{λ_{1}} = R (\frac{1}{1^{2}} - \frac{1}{2^{2}})$

= R $(1 - \frac{1}{4})$

$\frac{1}{λ_{1}} = \frac{3 R}{4}$

For first line of Paschen series,

$n_{1} = 3 and n_{2} = 4$

$\frac{1}{λ_{2}} = R (\frac{1}{3^{2}} - \frac{1}{4^{2}})$

= R $(\frac{1}{9} - \frac{1}{16})$

⇒ $= \frac{7 R}{144}$

∴ $\frac{λ_{1}}{λ_{2}} = \frac{7 R}{144} \times \frac{4}{3 R}$

$\frac{λ_{1}}{λ_{2}} = \frac{7}{108}$