Stern-Gerlach Spin Quantization

What you are seeing: a beam of neutral atoms of angular momentum $J$ entering a magnet with field gradient $\mathrm{d}B_z/\mathrm{d}z$ . The transverse force $F_z = \mu_z \mathrm{d}B_z/\mathrm{d}z$ deflects each atom by an amount proportional to its projection $m_J$ . The screen on the right shows $2J+1$ discrete spots (quantum) or a continuous band (classical, for comparison)

Figure 1. Stern-Gerlach apparatus: oven, magnet pair with B_z gradient, and screen. Atoms are deflected by F_z = mu_z dB_z/dz; the screen histogram shows 2J+1 discrete spots (quantum) versus a continuous band (classical). Method: classical Newton with quantized m_J.

spin J1/2

gradient dB/dz0.20

atom rate6

modeQ

WHAT TO TRY

Switch between quantum and classical mode: a classical magnetic moment would smear into a continuous band, but the quantum beam splits into exactly 2J+1 discrete spots, the 1922 result.
Change the spin J: the number of spots jumps to 2J+1, so spin-1/2 gives two, spin-1 gives three, the direct readout of angular-momentum quantization.
Raise the field gradient dB/dz: the spots separate further, since the deflection is proportional to the gradient times the projected magnetic moment.