Larmor frequency

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fluidistic
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Homework Statement


Calculate Larmor frequency and the allowed values of the magnetic energy for an electron in a state n=2 of an hydrogen atom. Consider that there's an external magnetic field of intensity B=1T.


Homework Equations


No idea. I don't have any info on this in my classnotes. So I checked out http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/larmor.html#c1 but I get lost.


The Attempt at a Solution


From my understanding, in the state n=2 the electron can have either a "spin up" or "spin down" (though I never learned yet what is the spin). What I understand from my reading is that if there's an external magnetic field, the electron will suffer a torque and "precess" with the Larmor frequency. But I don't know how to relate this with the state n=2 in the hydrogen atom.
According to hyperphysics: [itex]\omega _{\text {Larmor}}=\frac{eB}{2m_e}[/itex].
 

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  • #3
fluidistic
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I appreciate your help but there's nothing that can help me there I think. I know that the magnetic field will causes more emission/absorption lines due to Zeenman effect but there's nothing said for "Larmor frequency" in wikipedia and the pictures of the links.
In hyperphysics I found the equation [itex]\Delta E = m_l \mu _B B[/itex]. Not sure this can help me. I also found [itex]\Delta E =g_L m_j \mu _B B[/itex].
I'm actually totally lost.
 
  • #4
fluidistic
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I think I got it.
Electron in state n=2 means that the quantum number m can only be -1,0 or 1.
Now I use the fact that [itex]\Delta E = \mu _B mB[/itex]. So I take m=1 for example so I get the value of [itex]\Delta E[/itex]. Then I also know that [itex]\Delta E = h \nu[/itex]. I just have to solve for [itex]\nu[/itex], this is Larmor frequency.
If I said something wrong please let me know.
 

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