# (a) What is the ionisation energy of a hydrogen atom that is in the n=6 excited state? (b) For a...

## Question:

(a) What is the ionisation energy of a hydrogen atom that is in the n=6 excited state?

(b) For a hydrogen atom , determine the ratio of the ionisation energy for the n=6 excited state to the ionisation energy for the ground state.

## Ionisation Energy

The ionisation energy of the hydrogen atom is inversely proportional to the square of the excited state. And it is given by the following equation

{eq}\displaystyle E = \dfrac{-13.6}{n^{2}} \ eV {/eq}

(a)

Now the Ionisation energy for the excited state (n) = 6

{eq}\displaystyle E_{6} = \dfrac{-13.6}{n^{2}} \eV \\ E_{6} = \dfrac{-13.6}{36} = -0.378 \ eV {/eq}

(b)

Now the energy for the ground state

{eq}\displaystyle E_{1} = -13.6 \ eV {/eq}

Now the ratio will be

{eq}\displaystyle \dfrac{E_{6}}{E_{1}} = \dfrac{-0.378}{-13.6} \\ \dfrac{E_{6}}{E_{1}} = \dfrac{1}{36} {/eq}