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?
Well, if you are climbing a flight of stairs..........
.........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
But when we raise the electron from