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?

1 Answer
Mar 11, 2017

Answer:

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?