NEET 2025 — Chemistry solution

NEET2025Chemistry

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

A
$\frac{1}{36}$
B
$\frac{1}{16}$
C
$\frac{1}{9}$
D
$\frac{1}{4}$

Solution

Using the Rydberg formula: $\frac{1}{λ} = R Z^{2} (\frac{1}{n _{1}^{2}} - \frac{1}{n _{2}^{2}})$ for hydrogen ( $Z = 1$ ).

For $n = 2 \to 3$ : $\frac{1}{λ _{1}} = R (\frac{1}{4} - \frac{1}{9}) = R \cdot \frac{5}{36}$ .

For $n = 4 \to 6$ : $\frac{1}{λ _{2}} = R (\frac{1}{16} - \frac{1}{36}) = R \cdot \frac{5}{144}$ .

$∴ \frac{λ _{1}}{λ _{2}} = \frac{5/144}{5/36} = \frac{36}{144} = \frac{1}{4}$ .

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