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

The wavelengths emitted are to lie in the Lyman series (infrared region).

Explanation:

When the electron collides, all its energy is passed to the hydrogen atom.

The energy of excitation to elevate the electron from ground to nth state is given by

$E=(13.6 \mathrm{eV}) \times\left(\frac{1}{1^{2}}-\frac{1}{n^{2}}\right)$

Substitute n = 2, we obtain

E  = 10.2 eV  

Substitute n = 3, we obtain

E'  = 12.08 eV  

Thus the atom will be moved to the second level of excited energy.

So there are transformations from n = 3 to n = 1 when it comes to ground state.

The wavelengths emitted are therefore to lie in the Lyman series (infrared region).