Question

Which wavelengths will be emitted by a sample of atomic hydrogen gas (in ground state) if electrons of energy 12.2 eV collide with the atoms of the gas?

Answer 1

As the electron collides, it transfers all its energy to the hydrogen atom.
The excitation energy to raise the electron from the ground state to the nth state is given by
$E=(13.6\mathrm{eV})\times \left(\frac{1}{1^2}-\frac{1}{n^2}\right)$
Substituting n = 2, we get
E = 10.2 eV
Substituting n = 3, we get
E' = 12.08 eV

Thus, the atom will be raised to the second excited energy level.
So, when it comes to the ground state, there is transitions from n = 3 to n = 1.
Therefore, the wavelengths emitted will lie in the Lyman series (infrared region).