Q 12-12-027JEE MainJEE Main 2026 (6 Apr, Shift 1)Medium
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:-
Answer: (D) $20$ and $27$
$p = \dfrac{h}{\lambda} \propto \dfrac{1}{\lambda} \propto \left(\dfrac{1}{2^2} - \dfrac{1}{n^2}\right)$.
First line ($n = 3$): $\dfrac{1}{4} - \dfrac{1}{9} = \dfrac{5}{36}$. Second line ($n = 4$): $\dfrac{1}{4} - \dfrac{1}{16} = \dfrac{3}{16}$.
$\dfrac{p_1}{p_2} = \dfrac{5/36}{3/16} = \dfrac{80}{108} = \dfrac{20}{27}$.
Solution by Sreeraj P, M.Sc Physics