# Calculate Larmor Freq. for Electron in n=2 of Hydrogen Atom

• fluidistic

Gold Member

## 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: $\omega _{\text {Larmor}}=\frac{eB}{2m_e}$.

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 $\Delta E = m_l \mu _B B$. Not sure this can help me. I also found $\Delta E =g_L m_j \mu _B B$.
I'm actually totally lost.

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 $\Delta E = \mu _B mB$. So I take m=1 for example so I get the value of $\Delta E$. Then I also know that $\Delta E = h \nu$. I just have to solve for $\nu$, this is Larmor frequency.
If I said something wrong please let me know.