Question

In a normal zeeman effect a single spectral line is split into three spectral lines of different wavelengths.why is this so?

Answer 1

The spin of the electron creates an intrinsic magnetic moment for the electron. In the presence of no magnetic field, an electron in, say, the n=2, l=1 state has three possible values (1, 0, -1) for the z-component of its angular momentum, and therefore three possible values for the z-component of its magnetic moment. Typically this does not change the energy of the electron and so transitions downward from these three states all release the same amount of energy, in the form of light of a single wavelength. However, in the presence of an applied magnetic field, the magnetic moment of the electron interacts with the field to very slightly change the energy of the electron, splitting the single line into three closely spaced ones.

Answer 2

More accurately, 1 0 and -1 are the possible values for the quantum number m, and
\[\hbar, 0, -\hbar\]
are the possible values for the momentum itself...