STERN-GERLACH EXPERIMENT

NORTH

SOUTHCollimated beam of Ag(g)atoms Magnetic Field

Z-direction ↑

STERN-GERLACH EXPERIMENT After passing through the magnetic field two

beams of Ag(g) atoms emerge – suggests that some sort of quantized angular momentum is associated with a charged particle (classically a range of deflections is expected). Can the deflection be due to an electron? Can the deflection be due, in particular, to orbital angular momentum?

STERN-GERLACH EXPERIMENT Silver has an odd number of electrons. The

usual table of l and ml values shows that orbital angular momentum cannot explain the Stern Gerlach experiment for Ag(g).

l mlEmergent Beams Expected

0 0 11 1,0,-1 32 2,1,0,-1,-2 5

STERN-GERLACH EXPERIMENT Neglecting history, we can write an electron

configuration for neutral Ag which also suggests that orbital angular momentum cannot account for the Stern Gerlach expt.

Ag: [Ar] 3d104s24p64d105s1

The lone electron is in an s orbital for which l = 0.

STERN-GERLACH EXPERIMENT FOR Ag

Again, for the lone unpaired electron in Ag we have l = 0.

Magnitude of orbital angular momentum “squared” = l (l +1)ħ2 = 0

Similarly LZ = ml ħ = 0 The z-component of angular momentum

determines how many “beams” we should see in the Stern-Gerlach experiment.

STERN-GERLACH EXPERIMENT

SPIN WAVE FUNCTIONS