Electron spin - energy difference between split levels?

In summary, the conversation discusses the interaction energy of an electron in an atom with a magnetic field and the energy difference between the two split states. The speakers also mention using equations to calculate the energy difference and discuss the best approach for solving the problem.
  • #1
accountkiller
121
0
I found the interaction energy U of an electron in an atom with orbital quantum number l=0 with a uniform 2.00-T magnetic field to be 1.159E-4 eV, now it asks what is the energy difference between the two split states?

We have short 3-point quizzes each day before lecture just to make sure that we read the section in the book because we will start talking about this new material in class. However, I don't see anything with energy difference information in this section in the book or in the MasteringPhysics side note.

The only thing close to is that there is an example for a 3p level of a sodium atom where you find energy E = hc/lambda of the two photonsbut then would my lambda be? I don't think that helps either.

I'd appreciate any help, thanks!
 
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  • #2
Was the interaction energy you found due to the electron spin? Does the spin up state have the same energy as the spin down state?
 
  • #3
Yeah... MasteringPhysics is amazingly bad.

The split states:
When you have an electron in an atom, it has some energy [tex]E_0[/tex] (lets say). In a magnetic field, because of the intrinsic spins of the electrons, they can either gain or lose the interaction energy with the magnetic field (in your case [tex]\Delta E \approx 1E-4[/tex]), thus the final split energies will be [tex]E = E_0 - \Delta E[/tex] and [tex]E = E_0 + \Delta E[/tex], what's the difference in energies between those two split states?
 
  • #4
Ah, thank you for those equations. But what is my E0? Using deltaE = 1.159*10^4, I just picked a random number for E0 (I used 5) then calculated 5 - deltaE and 5 + deltaE and took the difference, and I got the correct answer, 2.318*10-4. I take it this is probably no the scientific way to do it. What is?
 
  • #5
mbradar2 said:
Ah, thank you for those equations. But what is my E0? Using deltaE = 1.159*10^4, I just picked a random number for E0 (I used 5) then calculated 5 - deltaE and 5 + deltaE and took the difference, and I got the correct answer, 2.318*10-4. I take it this is probably no the scientific way to do it. What is?
Great question. Especially in physics, its best to set up your equations before plugging in values. This way you can see what aspects of the equations 'drop out' or cancel. Using the equations I gave you, try solving for the difference in energy levels (i.e. before plugging values in). See what you find
 

Related to Electron spin - energy difference between split levels?

1. What is meant by "electron spin" in relation to energy levels?

Electron spin refers to the intrinsic angular momentum of an electron, which can have either an "up" or "down" orientation. This spin determines the energy levels that an electron can occupy within an atom or molecule.

2. How does the energy difference between split levels affect the behavior of electrons?

The energy difference between split levels affects the behavior of electrons by determining the likelihood of an electron transitioning from one level to another. An electron will only transition to a lower energy level if it can emit the energy difference as a photon, or if it can absorb energy from an outside source to reach a higher energy level.

3. What causes the split levels in electron spin energy?

The split levels in electron spin energy are caused by the presence of a magnetic field. The magnetic field interacts with the spin of the electron, causing the energy levels to split into two sublevels.

4. How is the energy difference between split levels measured?

The energy difference between split levels can be measured using spectroscopy techniques. This involves shining a specific wavelength of light onto a sample and measuring the energy absorbed or emitted by the electrons as they transition between energy levels.

5. Can the energy difference between split levels be manipulated?

Yes, the energy difference between split levels can be manipulated by changing the strength of the magnetic field. This can be done using specialized equipment such as electromagnets. Additionally, the energy levels themselves can be manipulated by changing the composition of the material or the external conditions, such as temperature or pressure.

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