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?

Respuesta :

Explanation:

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

               E = [tex]\frac{13.6 eV}{n^{2}}[/tex]

or,          n = [tex]\sqrt{\frac{13.6}{E}}[/tex]

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

                   n = [tex]\sqrt{\frac{13.6}{E}}[/tex]

                      = [tex]\sqrt{\frac{13.6}{0.544 eV}}[/tex]

                      = 5

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