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?

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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?

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Answer 1 · 2017-03-11T21:13:36

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 $n = 1$ $n=1$ to $n = \infty$ $n=oo$ ; 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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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

Explanation:

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