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

[fluidistic]

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

 

[Spinnor]

See,

http://www.google.com/imgres?q=zeem...83&tbnw=144&start=0&ndsp=8&ved=1t:429,r:1,s:0

http://www.google.com/search?hl=en&...&um=1&ie=UTF-8&tbm=isch&source=og&sa=N&tab=wi

Good luck!

http://en.wikipedia.org/wiki/Zeeman_effect

http://www.google.com/webhp?hl=en#h...w.,cf.osb&fp=250116ba2d339486&biw=720&bih=426

 

[fluidistic]

See,

http://www.google.com/imgres?q=zeem...83&tbnw=144&start=0&ndsp=8&ved=1t:429,r:1,s:0

http://www.google.com/search?hl=en&...&um=1&ie=UTF-8&tbm=isch&source=og&sa=N&tab=wi

Good luck!

http://en.wikipedia.org/wiki/Zeeman_effect

http://www.google.com/webhp?hl=en#h...w.,cf.osb&fp=250116ba2d339486&biw=720&bih=426

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.

 

[fluidistic]

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.

 

[asteriatic]

To calculate the Larmor frequency for an electron in the n=2 state of a hydrogen atom, we need to first determine the electron's magnetic moment in this state. The magnetic moment of an electron is given by \mu =\frac{e\hbar}{2m_e} where e is the charge of an electron, \hbar is the reduced Planck's constant, and m_e is the mass of an electron.

In the n=2 state of a hydrogen atom, the electron's spin can have two possible values: +\frac{1}{2} and -\frac{1}{2}. This means that the magnetic moment of the electron in this state can have two possible values: +\frac{e\hbar}{4m_e} and -\frac{e\hbar}{4m_e}.

Next, we can calculate the Larmor frequency using the equation \omega _{\text {Larmor}}=\frac{\mu B}{\hbar}. Plugging in the known values, we get \omega _{\text {Larmor}}=\frac{eB}{2m_e}, which is the same as the equation given by hyperphysics.

For the allowed values of the magnetic energy, we can use the equation E=\mu B. Since the magnetic moment can have two possible values, the magnetic energy can also have two possible values: +\frac{e\hbar B}{4m_e} and -\frac{e\hbar B}{4m_e}. These are the allowed values of the magnetic energy for an electron in the n=2 state of a hydrogen atom in an external magnetic field of intensity B=1T.