# How do you calculate the Ionization energy of Hydrogen?

Feb 4, 2018

See the explanation that follows...

#### Explanation:

You are able to calculate the ionization energy of hydrogen because of a formula developed by Neils Bohr in his early quantum atom.

Besides his one postulate that limited a characteristic of the electron known as angular momentum, he used mostly classical mechanics to obtain a formula for the allowed energies of the hydrogen atom as

${E}_{n} = - \frac{1311 \frac{k J}{\text{mol}}}{n} ^ 2$

where $n$ was the number of the orbit (n=1 being the orbit closest to the nucleus). n could take on only integer values. The numerator
was obtained by inserting a number of physical constants that included the mass and charge of the electron.

So, with the electron in the ground state (lowest energy), the value of $n$ is 1, and the value of the energy of the atom was $- 1311 \frac{k J}{\text{mol}}$.

If the electron were to be removed from the atom, this corresponded to raising it past all possible values of $n$, (or to $n \rightarrow \infty$). At this point, the energy of the system is zero.

To determine the ionization energy, one had only to determine the difference between these two states:

$\Delta E = 0 - \left(- 1311\right) = + 1311 \frac{k J}{\text{mol}}$