# Stern-Gerlach Experimental Calculation

I've run into a problem which has been bugging me for days. I know its related to the Stern-Gerlach experiment about firing hydrogen through an inhomogeneous magnetic field, but all i can do is give a vague qualitative description of the answers, and not an actual numerical one (because I don't entirely know what equations should be useful).

I know theres stuff about magnetic moments and spin and dipole moments happening here, but I can't seem to reconcile all these ideas. I'm not looking for a raw solution (I still want to learn something), just pointers as to the physics that's happening here, and possibly what equations are useful. Thanks.

Consider a well-collimated beam of hydrogen atoms in their ground state (ie with zero orbital angular momentum and spin = 1/2) in which the atoms are in thermal equilibrium at a temperature of 600K. The beam enters a region of length 9cm, in which there is a strong magnetic field with a gradient of 2x10³T/m perpendicular to the axis of the beam. After leaving this region the beam travels 1.2m to a screen.
1. What distribution of hydrogen atoms would one observe at the detector?
2. How is this different from classical expectations?
3. How is this different from non-relativistic quantum predictions?
4. Where will the beam appear on the screen?
5. How does this provide evidence for a "spin g-factor" of 2?

I know (basically) that because of the inhomogeneous magnetic field, the atoms experience a force in the z-direction (vertically). Classically, theres stuff about all possible ranges of spin/momentum (or something) which would give a continuous band on the screen. Quantum mechanically, theres stuff about quantized spins that will only allow discrete outcomes, and i think the relativistic bit refers to the spin quantum number, m_s, but it might not. I can kinda handle the first three parts (if I'm even on the right track), but the fourth part - actually finding where the beam will appear - is a bit mysterious at the moment.

Thanks again.

For 4, use the equation for the force on a dipole $$F=(\mu\cdot\nabla)B$$,