A magnetic field will be said to be weak in case of Zeeman effect, if the total spread of the Zeeman pattern of each line is small relative to the spacing of the line themselves. It has been observed that if the B is made sufficiently strong, then the anamalous Zeeman splitting will revert to the normal Zeeman triplet through coalscence or disappearance of certain lines. This effect is known as Paschen Back effect. When magnetic field becomes very strong then the coupling between ‘l’ and’s’ breaks down and they quantized separately, discarding the significance of J. L and S precess separately about B independently. Therefore the energy change due to B will be result of precession of L about B and procession of 5 about B separately.
In huge magnetic field the spin-orbit interaction is swamped and hence the quantum numbers n, l, ml, ms with the axis parallel to B. Under these circumstances
(l)z = mlh and (s)z = msh
Since µz does not vary appreciably with further increase in B, the energy of the atom
E = E0 + µB B(mj + ms) … (1)
and change in energy
ΔE = µB B(mj + ms) … (2)
From equation (2) one can observe that B splits from single original level into several levels, each of which is characterized by (mj + ms) Now (mj + ms) can take any integral value from (l + 1) to – (l + I), when ml = l, and ms = 1/2, i.e., total 2l + 3 levels in all. However if l=0, there are only two levels with mj + ms = ± 1. Here (mj + ms) is known as strong field quantum number.
Consider transition from l = 1 to l = 0
The selection rules are Δl = 1, Δmj = 0, 1
and Δms = 0