?The Zeeman effect is the modification of an atomic spectrum by the application of a

Chapter 8, Problem P8C.10

(choose chapter or problem)

The Zeeman effect is the modification of an atomic spectrum by the application of a strong magnetic field. It arises from the interaction between applied magnetic fields and the magnetic moments due to orbital and spin angular momenta (recall the evidence provided for electron spin by the Stern–Gerlach experiment, Topic 8B). To gain some appreciation for the so-called normal Zeeman effect, which is observed in transitions involving singlet states, consider a p electron, with \(l\) = 1 and \(m_{1}\) = 0, \(\pm 1\). In the absence of a magnetic field, these three states are degenerate. When a field of magnitude \(\mathcal{B}\) is present, the degeneracy is removed and it is observed that the state with \(m_{1}\) = +1 moves up in energy by \(\mu_{\mathrm{B}} \mathcal{B}\), the state with ml = 0 is unchanged, and the state with \(m_{1}\) = −1 moves down in energy by \(\mu_{\mathrm{B}} \mathcal{B}\), where \(\mu_{\mathrm{B}}=e \hbar / 2 m_{e}=9.274 \times 10^{-24} \mathrm{~J} \mathrm{~T}^{-1}\) is the ‘Bohr magneton’. Therefore, a transition between a \({ }^{1} \mathrm{~S}_{0}\) term and a \({ }^{1} \mathrm{~P}_{1}\) term consists of three spectral lines in the presence of a magnetic field where, in the absence of the magnetic field, there is only one. (a) Calculate the splitting in reciprocal centimetres between the three spectral lines of a transition between a \({ }^{1} \mathrm{~S}_{0}\) term and a \({ }^{1} \mathrm{~P}_{1}\) term in the presence of a magnetic field of 2T (where 1T = 1 kg \(\mathrm{s}^{-2} \mathrm{~A}^{-1}\)). (b) Compare the value you calculated in (a) with typical optical transition wavenumbers, such as those for the Balmer series of the H atom. Is the line splitting caused by the normal Zeeman effect relatively small or relatively large?

Text Transcription:

I

M_1

pm1

B

mu_BB

mu_B=e/2 m_e=9.27410^-24JT^-1

^1S_0

^1P_1

s^-2A^-1