Wave number of an electronic transition occuring from second orbit to first orbit of hydrogen atom is X1 . Wave number of an electronic transition occuring from fourth orbit to second orbit of hydrogen atom is X2. Ratio of X1 : X2 is

ν-=1λ=RH1n12−1n22X1X2=112−122122−142X1X2=34×163X1X2=4

Wave number of an electronic transition occuring from second orbit to first orbit of hydrogen atom is X1 . Wave number of an electronic transition occuring from fourth orbit to second orbit of hydrogen atom is X2. Ratio of X1 : X2 is

ν-=1λ=RH1n12−1n22X1X2=112−122122−142X1X2=34×163X1X2=4

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Wave number of an electronic transition occuring from second orbit to first orbit of hydrogen atom is X₁ . Wave number of an electronic transition occuring from fourth orbit to second orbit of hydrogen atom is X₂. Ratio of X₁ : X₂ is

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2 : 1

1 : 2

4 : 1

1 : 4

answer is C.

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Detailed Solution

$\begin{array}{l} \bar{ν} = \frac{1}{λ} = R_{H} (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}) \\ \frac{X_{1}}{X_{2}} = \frac{(\frac{1}{1^{2}} - \frac{1}{2^{2}})}{(\frac{1}{2^{2}} - \frac{1}{4^{2}})} \\ \frac{X_{1}}{X_{2}} = \frac{3}{4} \times \frac{16}{3} \\ \frac{X_{1}}{X_{2}} = 4 \end{array}$