1. 1/36 2. 1/16 3. 1/9 4. 1/4

Answer: 4. 1/4 Key idea: absorbed wavelength is inversely proportional to the energy gap, 1/λ∝(1/n₁²-1/n₂²) . For 2→3 : 1/4-1/9=5/36 , so λ₁∝36/5 . For 4→6 : frac116-frac136=5/144 , so λ₂∝144/5 . λ₁/λ₂=36/144=1/4 . Option (4).

Topic: Electromagnetic radiation, photoelectric effect, hydrogen spectrum· Atomic Structure

The ratio of the wavelengths of the light absorbed by a Hydrogen atom when it undergoes n=2 → n=3 and n=4 → n=6 transitions, respectively, is

1. \(\frac{1}{36}\)

2. \(\frac{1}{16}\)

3. \(\frac{1}{9}\)

4. \(\frac{1}{4}\)

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Answer: 4. \(\frac{1}{4}\)

Key idea: absorbed wavelength is inversely proportional to the energy gap, \(\frac{1}{\lambda}\propto\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)\).

For \(2\to3\): \(\frac14-\frac19=\frac{5}{36}\), so \(\lambda_1\propto\frac{36}{5}\).
For \(4\to6\): \(\frac1{16}-\frac1{36}=\frac{5}{144}\), so \(\lambda_2\propto\frac{144}{5}\).

\(\frac{\lambda_1}{\lambda_2}=\frac{36}{144}=\frac14\). Option (4).

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The ratio of the wavelengths of the light absorbed by a Hydrogen atom when it undergoes n=2 → n=3 and n=4 → n=6 transitions, respectively, is

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