Stern-gerlach with hydrogen atoms

[cragar]

I was looking through a physics book that has the answers in the back.
this is not homework. It asks about a neutral beam of hydrogen atoms going into a strong non-constant B field. It asks how many ways will the beam split. It says the answer is 2.
Why is the answer not 3. spin 1, spin 0, spin -1. if we consider the spin of the proton and the spin of the electron. we should have 3 cases. both spin up, both spin down, and then opposite spins.

 

[mfb]

Compare the magnetic moments of electron and proton. One of them is negligible.

 

[cragar]

I see the formula for the the magnetic moment has the mass in the denominator, so it will be a lot smaller for the proton. But why can't I consider the magnetic moment of the whole atom and for the mass term use the mass of the hydrogen atom. Because the electron and proton are one connected system.

 

[mfb]

Because the electron and proton are one connected system.

Yes, and the system has one spin, but this spin is the sum of two parts - a large part and a tiny part.

 

[jtbell]

I would say rather that the system has a total magnetic moment, which is the sum of a large part (from the electron) and a small part (from the proton). For magnetic interactions, what directly matters is the magnetic moment, not the spin. The magnetic moment of a particle depends on the spin, of course, but it also depends on other factors.

 

[Meir Achuz]

I see the formula for the the magnetic moment has the mass in the denominator, so it will be a lot smaller for the proton. But why can't I consider the magnetic moment of the whole atom and for the mass term use the mass of the hydrogen atom. Because the electron and proton are one connected system.

Magnetic effect on the electron is much larger than the magnetic interaction between the electron and proton. Consequently, the electron and proton are no longer one system.