Question

An electron is excited from the n=1 ground state to the n=3 state in a hydrogen atom. Does it take more energy to ionize (completely remove) the electron from n=3 than from the ground state?

Answer 1

Well, if you are climbing a flight of stairs..........

Explanation:

.........does it take you more energy to climb from the bottom of the stairs, than from 3 steps up the flight of stairs? Quite clearly it does.

When we ionize an electron, essentially we raise it from `n=1` to `n=oo`; now clearly this is going to be endothermic:

`"Atom, (n=1),"+Delta_1 rarr "Atom"^+(n=oo) + e^-`

But when we raise the electron from `n=1` to `n=3`, then clearly this also will be endothermic:

`"Atom, (n=1),"+Delta_2 rarr "Atom"^+(n=3)+ e^-`

`"Atom, (n=3),"+Delta_3 rarr "Atom"^+(n=oo) + e^-`

Clearly, `Delta_2+Delta_3=Delta_1` by considerations of conservation of energy. And thus, necessarily, `Delta_1>Delta_3` (and the difference is `Delta_2`). Are you happy with this treatment?