Zeeman Effect for a Muon: Differences Compared to Ordinary Hydrogen Atoms

In summary, the Zeeman Effect in an atom with a proton nucleus and an orbiting negatively charged muon will have a smaller energy difference compared to ordinary hydrogen atoms. This is due to the muon's greater mass and spin, which does not affect the equation for the energy difference. The muon has the same spin as an electron.
  • #1
pka
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Homework Statement


Consider an atom composed of a proton nucleus and an orbiting negatively charged muon (which has a mass of 207*(mass of an electron)). What difference, if any, would you expect between the Zeeman Effect in such atoms and in ordinary hydrogen atoms? (Hint: the muon has spin -1/2, but a greater mass than the electron).


What I've done:
The change in energy for a hydrogen atom according to the Zeeman effect (or because of it) is: delta E = 2*(bohr magneton, Mb)*(magnetic field).

This is where I am getting a little confused...For the muon, the energy difference will not be the same. What I'm having trouble with is the equation for which to use in order to determine the energy difference for the muon. What I've come up with is this:

Energy difference = 2*[ (e*h-bar)/ (2*207*mass of an electron) ]*(magnetic field)
Is this correct? What makes me unsure is the fact that the muon now has spin (not just a greater mass) so shouldn't my energy difference also be multiplied by the spin of the muon?

Assuming that both the hydrogen atom and the muon are in a uniform magnetic field of 1 Tesla and Mb = [(e*h-bar)/ (2*mass of an electron)] = 9.274 x 10^-24 J/T.

My conclusion is that the energy difference for the muon will be smaller than that for the hydrogen atom because splitting is greater for the atom with spin. Also, the muon has greater mass so the energy difference will end up being closer to zero than the hydrogen atom and thus being smaller and leading to a greater splits in the spectra when you look at the little lines for the muon. On the other hand, the hydrogen atom will simply have three splits on its spectra.

Any help or advice anyone can offer would be fantastic! If I'm thinking about this as I shouldn't be I'd greatly appreciate it with anyone could point me in the right direction. Many thanks in advance.
 
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  • #2
pka said:

Homework Statement


Consider an atom composed of a proton nucleus and an orbiting negatively charged muon (which has a mass of 207*(mass of an electron)). What difference, if any, would you expect between the Zeeman Effect in such atoms and in ordinary hydrogen atoms? (Hint: the muon has spin -1/2, but a greater mass than the electron).


What I've done:
The change in energy for a hydrogen atom according to the Zeeman effect (or because of it) is: delta E = 2*(bohr magneton, Mb)*(magnetic field).

This is where I am getting a little confused...For the muon, the energy difference will not be the same. What I'm having trouble with is the equation for which to use in order to determine the energy difference for the muon. What I've come up with is this:

Energy difference = 2*[ (e*h-bar)/ (2*207*mass of an electron) ]*(magnetic field)
Is this correct? What makes me unsure is the fact that the muon now has spin (not just a greater mass) so shouldn't my energy difference also be multiplied by the spin of the muon?
No, you don't have to worry about the spin. The muon has the same spin as an electron.
 
  • #3
Alrighty then! Sounds good to me. So I've got the right idea about the rest of the problem? Thanks so much. :D Fantastic!
 

1. What is the Zeeman Effect for a Muon?

The Zeeman Effect for a Muon refers to the phenomenon where the energy levels of a muon (a subatomic particle with a negative charge) split into multiple levels when placed in a magnetic field.

2. How does the Zeeman Effect for a Muon occur?

The Zeeman Effect for a Muon occurs due to the interaction between the magnetic field and the magnetic dipole moment of the muon. This causes the energy levels to split, resulting in multiple spectral lines.

3. What is the significance of the Zeeman Effect for a Muon?

The Zeeman Effect for a Muon is significant because it provides valuable information about the magnetic properties of the muon and its behavior in a magnetic field. It also has applications in fields such as particle physics and quantum mechanics.

4. Is the Zeeman Effect for a Muon the same as the Zeeman Effect for an electron?

No, the Zeeman Effect for a Muon is not the same as the Zeeman Effect for an electron. While they both involve the splitting of energy levels in a magnetic field, they occur due to different interactions and have different energy levels and spectral lines.

5. Can the Zeeman Effect for a Muon be observed in nature?

Yes, the Zeeman Effect for a Muon has been observed in various experiments and is a well-established phenomenon in the scientific community. It has also been observed in nature, such as in the study of cosmic rays and in nuclear magnetic resonance (NMR) spectroscopy.

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