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?

Md Ariful Islam

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Md Ariful Islam

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.........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?

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