A hydrogen atom is in its ground state. Which of the following photons can be absorbed by it?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A photon of energy 12.09 eV
An atom takes up a photon whole. So an atom in its ground state absorbs a photon only if the photon energy equals the gap between the ground level and a higher level. It can also absorb a photon of 13.6 eV or more, which is enough to free the electron. With \( E_n=-13.6\,\mathrm{eV}/n^{2} \), the steps up from the ground state are:
10.2 eV (to n = 2)
12.09 eV (to n = 3)
12.75 eV (to n = 4)
13.06 eV (to n = 5), and so on.
Option (1) A photon of energy 3.4 eV — Incorrect. 3.4 eV would free an electron already in the n = 2 level. But from the ground state, even the smallest step up needs 10.2 eV.
Option (2) A photon of energy 10.0 eV — Incorrect. It is less than the 10.2 eV gap to the first excited state. A photon cannot give only part of its energy to the atom.
Option (3) A photon of energy 12.09 eV — Correct. This is the gap between the n = 1 and n = 3 levels, so the photon raises the atom to its second excited state:
\( \begin{aligned} E_3-E_1 &= -1.51\,\mathrm{eV}-(-13.6\,\mathrm{eV}) \\ &= 12.09\,\mathrm{eV} \end{aligned} \)
Option (4) A photon of energy 13.0 eV — Incorrect. It lies between the 12.75 eV and 13.06 eV steps, so it matches no level difference. It is also less than the 13.6 eV needed to free the electron.
NCERT (2026-27):
The Line Spectra of the Hydrogen Atom – “… But when an atom absorbs a photon that has precisely the same energy needed by the electron in a lower energy state to make transitions to a higher energy state, the process is called absorption.”