The ratio of momentum of the photons of the $1^{\text{st}}$ and $2^{\text{nd}}$ line of Balmer series of Hydrogen atoms is $\alpha / \beta$. The possible values of $\alpha$ and $\beta$ are :-

JEE Main · 2026 · 06 Apr 2026 · Shift 1 · Modern Physics

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✓ Correct

Answer: (D)

Solution

Photon momentum is

p = \frac{h}{λ} \propto \frac{1}{λ}

. For the first Balmer line (

n = 3 \to 2

\frac{1}{λ _{1}} = R (\frac{1}{4} - \frac{1}{9}) = \frac{5 R}{36}

; for the second (

n = 4 \to 2

\frac{1}{λ _{2}} = R (\frac{1}{4} - \frac{1}{16}) = \frac{3 R}{16}

. The momentum ratio is

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

. Hence

α = 20

and

β = 27

JEE Main · 2026 · 06 Apr 2026 · Shift 1 · Single correct option

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