Q 12-12-051JEE MainJEE Main 2024 (29 Jan, Shift 1)Medium
When a hydrogen atom going from $n = 2$ to $n = 1$ emits a photon, its recoil speed is $\dfrac x5\ \text{m s}^{-1}$, where $x =$ ______. (Use: mass of hydrogen atom $= 1.6\times10^{-27}\ \text{kg}$, charge of electron $e = 1.6\times10^{-19}\ \text{C}$)
Numerical value type. Enter your answer.
Answer: 17
Photon energy: $E = 13.6\left(1 - \dfrac14\right) = 10.2\ \text{eV}$.
The atom recoils with the photon's momentum $p = E/c$:
$$v = \frac{E}{mc} = \frac{10.2\times1.6\times10^{-19}}{1.6\times10^{-27}\times3\times10^8} = 3.4\ \text{m s}^{-1} = \frac{17}{5}\ \text{m s}^{-1}$$
So $x = 17$.
Solution by Sreeraj P, M.Sc Physics