# What is the ionization energy of a hydrogen atom that is in the n = 6 excited state?

##### 1 Answer

#### Answer:

#### Explanation:

The Rydberg Expression is given by:

The energy levels converge and coalesce:

At higher and higher values of

The Rydberg Expression refers to emission where an electron falls from a higher energy level to a lower one, emitting a photon.

In this case we can use it to find the energy required to move an electron from

The expression now becomes:

Since

To convert this into energy we use the Planck expression:

You'll notice from the graphic that the energy of the

This means the energy to remove it will be

To convert this to Joules you multiply by the electronic charge

As you can see my calculated value is very close to this.

This is the energy required to ionise a single atom. To get the energy required to ionise a mole of atoms we multiply by the Avogadro Constant: