Question

A spectral line caused by the transition `.^(3)D_(1) rarr ^(3)P_(0)` experiences the Zeeman splitting in a weak magnetic field. When observed at right angles to the magnetic field direction, the interval between the neighbouring components of the split line is `Delta omega= 1.32.10^(10) s^(-1)`. Find the magnetic field induction `B` at the point where the source is located.

Answer 1

The `.^(3)P_(0)` term does not split. The `.^(3)D_(1)` term splits into 3 lines corresponding to the shift.
`DeltaE= -gmu_(B)BM_(Ƶ)`
with `M_(Ƶ)=+- 1,0`. The interval between neighbouring components is then given by
`ħ Delta omega= g mu_(B)B`
Hence `B=(ħDelta omega)/(gmu_(B))`
Now for the `.^(3)D_(1)` term `g=1+(1xx2+1xx2-2xx)/(2xx1xx2)=1+(4-6)/(4)=(1)/(2)`
Substitution gives `B= 3.00KG= 0.3T`.