JEE Main 2025 Jan 23 Shift 1, Chemistry Q2: Bohr's Atomic Model

JEE Main2025Jan 23, Shift 1Chemistry

Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral line of H atom is suitable for this ?

Given: Rydberg constant

$R_{H} = 1 0^{5} cm^{- 1}$ , $h = 6.6 \times 1 0^{- 34}$ J s, $c = 3 \times 1 0^{8}$ m/s

Solution

Convert the wavelength: $λ = 900$ nm $= 9 \times 1 0^{- 5}$ cm.

For hydrogen ( $Z = 1$ ), the Rydberg formula gives:

$\frac{1}{λ} = R_{H} (\frac{1}{n _{1}^{2}} - \frac{1}{n _{2}^{2}})$

$\Rightarrow \frac{1}{n _{1}^{2}} - \frac{1}{n _{2}^{2}} = \frac{1}{λ R _{H}} = \frac{1}{( 9 \times 1 0 ^{- 5} ) ( 1 0 ^{5} )} = \frac{1}{9}$

The cleanest solution is $n_{1} = 3$ , $n_{2} = \infty$ (since $\frac{1}{9} - 0 = \frac{1}{9}$ ).

A transition terminating at $n = 3$ belongs to the Paschen series, so the matching line is $\infty \to 3$ .

Concept behind this question

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