Q 12-12-113JEE MainJEE Main 2019 (11 Jan, Shift 1)Medium
A hydrogen atom, initially in the ground state, is excited by absorbing a photon of wavelength $980$ Å. The radius of the atom in the excited state, in terms of Bohr radius $a_0$, will be:
Answer: (C) $16a_0$
Photon energy:
$$E = \frac{12400}{980}\ \text{eV} \approx 12.65\ \text{eV}$$
Absorption from $n = 1$ needs $13.6\left(1 - \dfrac1{n^2}\right)$ eV. This is $12.09$ eV for $n = 3$ and $12.75$ eV for $n = 4$; the photon energy is closest to $n = 4$.
$$r_n = n^2a_0 = 16a_0$$
Solution by Sreeraj P, M.Sc Physics