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In the hydrogen atom spectrum $λ_{3 - 1} and λ_{2 - 1}$ represent wavelengths emitted due to transition from second and first excited states to the ground state respectively. The value of $\frac{λ_{3 - 1}}{λ_{2 - 1}}$ IS

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4/9

27 / 32

9/4

32/27

answer is A.

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Detailed Solution

$\frac{1}{λ_{3 - 1}} = R (\frac{1}{1^{2}} - \frac{1}{3^{2}}) = \frac{8 R}{9} \frac{1}{λ_{2 - 1}} = R (\frac{1}{1^{2}} - \frac{1}{2^{2}}) = \frac{3 R}{4} \Rightarrow \frac{λ_{3 - 1}}{λ_{2 - 1}} = \frac{27}{32}$

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