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Q.

Suggest two transitions in hydrogen spectrum for which the wave number ratio is 108 : 7

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a

$2 \to 1; 3 \to 1$

b

$2 \to 1; 5 \to 4$

c

$2 \to 1; 4 \to 1$

d

$2 \to 1; 4 \to 3$

answer is B.

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Detailed Solution

$\bar{v} = R [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}] \bar{v_{1}} (2 \to 1) = R \frac{3}{4} \bar{v_{2}} (4 \to 3) = R [\frac{1}{3_{1}^{2}} - \frac{1}{4_{2}^{2}}] \frac{\bar{v_{1}}}{\bar{v_{2}}} = \frac{R \frac{3}{4}}{R \frac{7}{16 \times 9}} = \frac{108}{7}$

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Suggest two transitions in hydrogen spectrum for which the wave number ratio is 108 : 7