Energy levels of hydrogen in atomic units

In summary, the conversation discusses the effective potential for a hydrogen atom in atomic units and its relation to the energy levels for different values of the quantum number l. It is explained that the effective potential is the sum of the actual potential and the centrifugal repulsion. A plot of the potential for l=0,1,2,3 is shown and the energy levels for n=2,3,4 are marked. It is then discussed why, for a given n, l cannot be larger than n-1. The correct energy levels in atomic units are given as E = -\frac{1}{2n^{2}}, which explains why l<=n-1 and the energy levels intersect the curves for l<=n-1
  • #1
russdot
16
0
[solved] Energy levels of hydrogen in atomic units

Homework Statement


The effective potential for a hydrogen atom can be thought of as the actual potential plus the centrifugal repulsion, written as:
[tex]V_{eff} = -\frac{1}{r} + \frac{l (l+1)}{2r^{2}}[/tex]
Remembering that you are working in atomic units, make a plot of V_eff(r) for l=0,1,2,3. Mark the energy levels for n=2,3,4. Explain why, for a given n, l cannot be larger than n-1.

The attempt at a solution
I have plotted the potentials for l=0,1,2,3 here: http://img385.imageshack.us/my.php?image=plotte7.gif"

I used [tex]E=-\frac{1}{n^{2}}[/tex] for the energy levels in atomic units (is this correct?)
As far as explaining why l <= n-1, I thought that because the energy levels would intersect the curves for l <= n-1 and the potential energies with l>=n would be unbound so that l cannot be larger than n-1. However, this does not seem to be the case from the plot I've constructed. I hope the energies I've used are incorrect, because I can't seem to extract the answer out of my plot??
Thanks in advance!

EDIT:
I realized the energy levels should be : [tex]E = -\frac{1}{2n^{2}}[/tex]
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
for the energy levels in atomic units. With this, my plot makes sense and l cannot be larger than n-1 because the energy levels will intersect the curves for l<=n-1, but will be unbound for l>=n.
 

1. What are atomic units?

Atomic units are a system of measurement commonly used in physics and chemistry to simplify calculations involving the properties of atoms and molecules. They are based on fundamental physical constants such as the mass and charge of an electron, and are used to express quantities in terms of these constants.

2. How are the energy levels of hydrogen in atomic units calculated?

The energy levels of hydrogen in atomic units are calculated using the Rydberg formula, which is a mathematical equation that relates the energy of an electron in a hydrogen atom to its principal quantum number. The energy levels are also influenced by the mass and charge of the electron, as well as the distance between the electron and the nucleus.

3. Why are atomic units used to study the energy levels of hydrogen?

Atomic units are used to study the energy levels of hydrogen because they provide a more convenient and efficient way of representing the complex interactions between the electron and the nucleus. They also allow for simpler and more accurate calculations compared to using traditional units of measurement.

4. What is the significance of the energy levels of hydrogen in atomic units?

The energy levels of hydrogen in atomic units have significant implications in understanding the behavior and properties of atoms and molecules, as well as in various areas of physics and chemistry. They also play a crucial role in the study of quantum mechanics and the development of new technologies, such as quantum computing.

5. Can the energy levels of hydrogen in atomic units be experimentally measured?

Yes, the energy levels of hydrogen in atomic units can be experimentally measured using various techniques, such as spectroscopy. These measurements can be compared to the theoretical calculations to validate the accuracy and reliability of the atomic unit system.

Similar threads

  • Advanced Physics Homework Help
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
2
Views
793
  • Advanced Physics Homework Help
Replies
4
Views
2K
  • Advanced Physics Homework Help
Replies
2
Views
1K
  • Advanced Physics Homework Help
Replies
8
Views
1K
  • Quantum Physics
Replies
2
Views
1K
  • Advanced Physics Homework Help
Replies
5
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
14
Views
2K
Back
Top