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?

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?

Serenity Allen · Accepted Answer

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

It's obvious that climbing a flight of stairs from the bottom requires more energy than climbing it from three steps up. 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?

Avery Adams · Answer

undefined Yes, it takes more energy to ionize the electron from the n=3 state than from the ground state (n=1) in a hydrogen atom.