Question

If a hydrogen atom has its electron in the n = 4 state, how much energy in eV is needed to ionize it?

Short answer

The energy needed to ionize hydrogen atom is 0.85 eV.

Step-by-step solution

Definition of ionisation energy

The energy that is enough to separate the electron in the last shell of the atom also called valance electron is the ionization energy.

Given information and formula to be used

Consider the hydrogen atom has 4 states.

Consider the formula for the ionization energy as follows:

\({E_n} = \frac{{13.6\;{\rm{eV}}}}{{{n^2}}}\)

Here, \({E_n}\) is the ionization energy and nis the energy level.

Determine the energy in eV needed to ionize the hydrogen atom which has its electron in the n=4 state. 

Substitute 4 for nand determine the ionisation energy.

\(\begin{array}{c}{E_n} = \frac{{13.6\;{\rm{eV}}}}{{{4^2}}}\\{E_n} = \frac{{13.6\;{\rm{eV}}}}{{16}}\\{E_n} = 0.85\;{\rm{eV}}\end{array}\)

Therefore, the energy needed to ionize hydrogen atom is 0.85 eV.