Definition of energy level width

[Eitan Levy]

Homework Statement

An electron with energy $E_1=12.9124eV$ 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 $t$ the electron returns to n=1.

Find the width of energy level n

Relevant Equations

$E_n=-13.6\frac{z^2}{n^2}eV$

First, it is easy to see that n=4 after the collision because:

$E_1=-13.6\frac{1^2}{1^2}eV=-13.6eV$
$E_4=-13.6\frac{1^2}{4^2}eV=-0.85eV$
$E_5=-13.6\frac{z^2}{5^2}eV=-0.544eV$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 $\frac{h}{t}$ but the result didn't match.

What is this size and how to calculate it?

 

[kuruman]

This problem most likely involves the limiting uncertainty relation $\Delta E ~\Delta t \approx \dfrac {\hbar}{2}$.

 

[Eitan Levy]

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.

 

[kuruman]

My problem is that "width of energy level" was never defined in my class so I don't know how to proceed.

Would this link help?
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/parlif.html#c1