Q 12-12-110JEE MainJEE Main 2019 (8 Apr, Shift 1)Medium
Radiation coming from transitions $n = 2$ to $n = 1$ of hydrogen atoms fall on $\text{He}^+$ ions in $n = 1$ and $n = 2$ states. The possible transition of helium ions as they absorb energy from the radiation is
Answer: (B) $n = 2 \to n = 4$
Photon energy from hydrogen: $13.6\left(1 - \frac14\right) = 10.2\ \text{eV}$.
For $\text{He}^+$, $E_n = -\dfrac{54.4}{n^2}\ \text{eV}$: $E_1 = -54.4$, $E_2 = -13.6$, $E_3 = -6.04$, $E_4 = -3.4$, $E_5 = -2.18\ \text{eV}$.
From $n = 2$ to $n = 4$: $-3.4 - (-13.6) = 10.2\ \text{eV}$, an exact match. No other listed transition needs $10.2\ \text{eV}$.
Solution by Sreeraj P, M.Sc Physics