# Definition of energy level width

• Eitan Levy
In summary, the conversation discusses the calculation of energy levels after a collision, specifically the case where n=4. The definition of the width of an energy level is brought up, but there is no clear definition. The speaker tried using an online source but the results did not match. The conversation ends with a suggestion to use a link for further help.
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?

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

Last edited:
kuruman said:
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.

## 1. What is the definition of energy level width?

The energy level width refers to the range of energies that an electron can have within a specific energy level in an atom. It is a measure of the uncertainty in the energy of the electron.

## 2. How is energy level width related to the stability of an atom?

The energy level width is directly related to the stability of an atom. A smaller energy level width indicates a more stable atom, as the electrons have a more defined energy state and are less likely to jump to a different energy level.

## 3. What factors affect the energy level width of an atom?

The energy level width of an atom is affected by the number of electrons in the atom, the strength of the nuclear charge, and the distance between the nucleus and the electrons.

## 4. How is the energy level width measured?

The energy level width is typically measured using spectroscopy techniques, such as photoelectron spectroscopy or x-ray absorption spectroscopy. These methods involve bombarding the atom with energy and measuring the resulting changes in the electron energy levels.

## 5. How does the energy level width change in different elements?

The energy level width can vary greatly between different elements. Elements with more electrons tend to have larger energy level widths, as there are more possible energy states for the electrons. Additionally, the energy level width tends to decrease as you move from left to right on the periodic table, as the nuclear charge increases and the electrons are held more tightly to the nucleus.

• Introductory Physics Homework Help
Replies
5
Views
927
• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
21
Views
1K
• Introductory Physics Homework Help
Replies
15
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
4K
• Introductory Physics Homework Help
Replies
41
Views
2K
• Introductory Physics Homework Help
Replies
8
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
5K
• Introductory Physics Homework Help
Replies
7
Views
2K