Orbital Spin and External Magnetic Fields

In summary, a Hydrogen atom subjected to a strong magnetic field will split the 2p level into three levels due to the overwhelming spin-orbit coupling. The spacing between the levels can be calculated using the gLande equation and the splitting is only two-thirds of the 1s state. The spacing can be expressed in terms of Bext, e, me, and \hbar.
  • #1
ourio
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Homework Statement


A Hydrogen atom is subjected to a magnetic field strong enough to overwhelm the spin-orbit coupling. Into how many levels would the 2p level split? What would the spacing be in the terms of Bext, e, me, and [tex]\hbar[/tex]


Homework Equations


I know that I have to use the gLande equation:
U=gLande[tex]\frac{e}{2(me)}[/tex]mj[tex]\hbar[/tex]Bext


The Attempt at a Solution


I have a feeling that the 2p level will split into 3 levels, but I honestly don't know how to show it.

Any help will be greatly appreciated!
 
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  • #2
OK... I think I may have got some of it...
The 2p state of hydrogen has [tex]\ell[/tex]=1 with m[tex]\ell[/tex]=-1,0,1
So the 2p state splits into three levels by the external B.

Calculating the gLande factor for the 2p state as [tex]\frac{4}{3}[/tex] and the 1s state as 2, I find that the splitting of the 2p state is only [tex]\frac{2}{3}[/tex] that of the 1s state


SO... the spacing between the levels is:
[tex]\frac{e\hbar}{2m}[/tex]Bext[tex]\frac{2}{3}[/tex]

Does that look right to anybody out there? Help! :-(
 

1. What is orbital spin?

Orbital spin is the rotation of an object around an axis. This can refer to the spin of planets around the sun, electrons around an atom, or even galaxies rotating around a central point.

2. How does orbital spin affect an object?

Orbital spin can affect an object's stability, shape, and behavior. For example, the spin of planets around the sun determines their orbit and position in the solar system, while the spin of electrons around an atom governs its chemical properties.

3. What is an external magnetic field?

An external magnetic field is a magnetic field that is created by a source outside of the object or system being studied. This can be created by magnets or electric currents, and can influence the behavior of objects within its range.

4. How does an external magnetic field interact with orbital spin?

An external magnetic field can influence the direction and speed of an object's orbital spin. The strength and orientation of the magnetic field can determine the axis and rate of the spin, and can also cause the object to precess (wobble) or change its orbit.

5. What are some real-world applications of studying orbital spin and external magnetic fields?

Understanding the interactions between orbital spin and external magnetic fields is crucial in many fields, including astronomy, physics, and engineering. It is used in the design of spacecraft and satellites, as well as in medical imaging techniques such as MRI. It also plays a role in the behavior of particles in particle accelerators and is important in the study of quantum mechanics.

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