Definition of energy level width

  • Thread starter Eitan Levy
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  • #1
Eitan Levy
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Homework Statement:
An electron with energy [itex]E_1=12.9124eV [/itex] is involved in a collision with the electron in a hydrogen atom. The electron in the hydrogen atom before the collision is in energy level n=1 and the free electron gives it most energy possible, so that the electron in the hydrogen atom reaches energy level n.

After time [itex]t [/itex] the electron returns to n=1.

Find the width of energy level n
Relevant Equations:
[itex]E_n=-13.6\frac{z^2}{n^2}eV [/itex]
First, it is easy to see that n=4 after the collision because:

[itex]E_1=-13.6\frac{1^2}{1^2}eV=-13.6eV [/itex]
[itex]E_4=-13.6\frac{1^2}{4^2}eV=-0.85eV [/itex]
[itex]E_5=-13.6\frac{z^2}{5^2}eV=-0.544eV[/itex]


But, I never saw a definition for the width of an energy level.

I tried to use something I saw online that said it was equal to [itex]\frac{h}{t} [/itex] but the result didn't match.

What is this size and how to calculate it?
 

Answers and Replies

  • #2
kuruman
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This problem most likely involves the limiting uncertainty relation ##\Delta E ~\Delta t \approx \dfrac {\hbar}{2}##.
 
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  • #3
Eitan Levy
259
11
This problem most likely involves the limiting uncertainty relation ##\Delta E ~\Delta t \approx \dfrac {\hbar}{2}##.
My problem is that "width of energy level" was never defined in my class so I don't know how to proceed.
 

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