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ChemistryNEET 2025Bohr model and hydrogen spectrum

Structure of Atom

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

  1. A.136\dfrac{1}{36}
  2. B.116\dfrac{1}{16}
  3. C.19\dfrac{1}{9}
  4. D.14\dfrac{1}{4}✓

Solution

1λ∝1n12−1n22\frac{1}{\lambda} \propto \frac{1}{n_1^2} - \frac{1}{n_2^2}. For 2→32\to3: 14−19=536\frac14 - \frac19 = \frac{5}{36}. For 4→64\to6: 116−136=5144\frac{1}{16} - \frac{1}{36} = \frac{5}{144}. So λ2→3λ4→6=5/1445/36=14\frac{\lambda_{2\to3}}{\lambda_{4\to6}} = \frac{5/144}{5/36} = \frac{1}{4}.

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