The ratio of the wave numbers of the radiation corresponding to the third line of Balmer series and the second line of the Paschen series of hydrogen spectrum is:

21/16 x 9/4

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25/16 x 9/4

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21/25 x 9/4

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16/25 x 9/4

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Solution

The correct option is A 21/16 x 9/4
Use the formula,
Wavenumber = $R \times (1 / n_{1}^{2} - 1 / n_{2}^{2})$ .
For third line Balmer series $n_{1} = 2$ and $n_{2} = 5$ .
For second line Paschen series $n_{1} = 3$ and $n_{2} = 5$
Therefore the ratio is $(1 / 4 - 1 / 25) / (1 / 9 - 1 / 25)$ which equals
$21 / 16 \times 9 / 4$ .

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The ratio of the wave numbers of the radiation corresponding to the third line of Balmer series and the second line of the Paschen series of hydrogen spectrum is:

The correct option is A 21/16 x 9/4Use the formula,Wavenumber = R×(1/n21−1/n22).For third line Balmer series n1=2 and n2=5.For second line Paschen series n1=3 and n2=5Therefore the ratio is (1/4−1/25)/(1/9−1/25) which equals 21/16×9/4.