Question

Three photons coming from excited atomic-hydrogen sample are picked up. Their energies are 12.1 eV, 10.2 eV and 1.9 eV. These photons must come from

(a) a single atom
(b) two atoms
(c) three atoms
(d) either two atoms or three atoms

Answer 1

(d) either two atoms or three atoms

The energies of the photons emitted can be expressed as follows:
$13.6\left(\frac{1}{1^2}-\frac{1}{2^2}\right)\mathrm{eV}=10.2\mathrm{eV}$
$13.6\left(\frac{1}{1^2}-\frac{1}{3^2}\right)\mathrm{eV}=12.1\mathrm{eV}$
$13.6\left(\frac{1}{2^2}-\frac{1}{3^2}\right)\mathrm{eV}=1.9\mathrm{eV}$

The following table gives the transition corresponding to the energy of the photon:

Energy of photon	Transition
12.1 eV	n = 3 to n = 1
10.2 eV	n = 2 to n = 1
1.9 eV	n = 3 to n = 2

A hydrogen atom consists of only one electron. An electron can have transitions, like from n = 3 to n = 2 or from n = 2 to n = 1, at a time.

So, it can be concluded that the photons are emitted either from three atoms (when all the three transitions of electrons are in different atoms) or from two atoms (when an atom has n = 3 to n = 2 and then n = 2 to n = 1 electronic transition and the other has n = 3 to n = 1 electronic transition).