# Zeeman Effect in Mercury

My report on the Zeeman effect experiment for the lab course during the third year of my MSci. Might be of use to anyone taking the third year lab course but, otherwise, not terribly exciting.

Authors: Luke Pomfrey The Zeeman Effect causes the energy levels of electrons of some materials to split into a number of different levels when a sample of the material is placed in a magnetic field. This splitting of energy levels results in a splitting of the spectral lines emitted by the sample. In this experiment the splitting of spectral lines in Mercury, by the action of a magnetic field, was investigated. Both the energy change between each line and the polarisation of those lines was found and compared to theory. The results of the experiment show that the polarisation of the lines is indeed governed by the following conditions: For $\Delta m_{j} = 0$ (where $m_{j}$ is the magnetic quantum number, related to the component of angular momentum in the $z$-direction) the photons are linearly polarised along the direction of $\mathbf{B}$, these are termed $\pi$ lines. For $\Delta m_{j} = \pm 1$ the photons are circularly polarised along the direction of $\mathbf{B}$, these are termed $\sigma$ lines. The change in energy from the central line to the line in question should be given by the following.  \begin{equation*} \Delta E = \mu_{B} B \Delta \left( g_{j} m_{j} \right) \end{equation*}  Where, $\mu_{B}$ is the Bohr magneton, $B$ the magnetic field strength, and $g_{j}$ the $g$-factor. The results gained for these energy shifts are all to the same order of magnitude as the predicted values but all fall outside the error ranges on them. This would appear to have been caused by a systematic error, this will be discussed later. L. Pomfrey. Zeeman Effect in Mercury. November, 2007.
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