Question

A hydrogen atom in an excited state can be ionized with less energy than when it is in its ground state. What is n for a hydrogen atom if 0.544 eV of energy can ionize it?

Answer 1

Explanation:

It is known that formula for the ionization energy of hydrogen atom is as follows.

               E = $\frac{13.6 eV}{n^{2}}$

or,          n = $\sqrt{\frac{13.6}{E}}$

The value of energy is given as 0.544 eV. Therefore, we will calculate the value of n as follows.

                   n = $\sqrt{\frac{13.6}{E}}$

                      = $\sqrt{\frac{13.6}{0.544 eV}}$

                      = 5

Thus, we can conclude that n equals to 5 for a hydrogen atom if 0.544 eV of energy can ionize it.