JEE Main 2026 Apr 6 Shift 1, Physics Q19: The Line Spectra of the Hydrogen Atom

JEE Main2026Apr 6, Shift 1Physics

The ratio of momentum of the photons of the $1^{st}$ and $2^{nd}$ line of Balmer series of Hydrogen atoms is $α / β$ . The possible values of $α$ and $β$ are:

A
$27$ and $20$
B
$3$ and $16$
C
$5$ and $36$
D
$20$ and $27$

Solution

Photon momentum $p = h / λ$ , so $p \propto 1/ λ$ .

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

Balmer 2nd line ( $n = 4 \to 2$ ): $\frac{1}{λ _{2}} = R (\frac{1}{4} - \frac{1}{16}) = \frac{3 R}{16}$ .

$\frac{p _{1}}{p _{2}} = \frac{1/ λ _{1}}{1/ λ _{2}} = \frac{5 R /36}{3 R /16} = \frac{5 \cdot 16}{36 \cdot 3} = \frac{80}{108} = \frac{20}{27}$ .

$∴ α = 20, β = 27$ .

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JEE Main 2026 Apr 6 Shift 1, Physics Q19: The Line Spectra of the Hydrogen Atom

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