How Does the Stern-Gerlach Experiment Reveal Quantum Angular Momentum?

[Tony11235]

In a certain Stern-Gerlach experiment a bean of potassium atoms (mass: M=6.4673x10^-26 kg) emerges from an oven at a temperature of 150 C. That means that each potassium atom has a kinetic energy of 8.76x10^-21 J. The atoms pass through an inhomogeneous magnetic field, whose gradient is 1.2x10^2 T/cm for a distance of 2.0 cm, and continue through a free-field space of 10.0 cm before being deposited on a collector plate. What is the maximum distance between the two lines at the detector?

I'm not sure what is involved. I think my main problem is the picture. What two lines at the detector is the problem referring two? Right now I just can't focus I guess.

 

[Doc Al]

The potassium atoms have a magnetic moment (due to the electron spin), thus they will feel a net force in an inhomgeneous magnetic field. Classically, the component of the magnetic moment in the direction of the field gradient would take on a continuum of values. But quantum mechanically, the component of the magnetic moment is quantized to only two values (spin up or spin down); thus the beam of atoms is split in two, forming two "lines" on the plate.