Question

How does the splitting of the spectral lines take place in the Zeeman effect?

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Solution

Zeeman Effect:The splitting of a spectral line due to a magnetic field was first observed by the Dutch physicist P. Zeeman in 1896. Hence it is known Zeeman effect. H.A. Lorentz developed a classical theory of the effect which gave the same expression for the Zeeman splitting as the equation given below.$\overline{\nu }=\overline{{\nu }_{0}}+\frac{eB}{4{\mathrm{\pi m}}_{\mathrm{e}}\mathrm{c}}△{m}_{l}$ where ${\nu }_{0}=\frac{{E}_{nl}-{E}_{n\text{'}l\text{'}}}{2\mathrm{\pi c}\overline{)\mathrm{h}}}$ is the original wave number of the unsplitted spectral line.Here, $\overline{\nu }$ is the wave number of the resultant spectral line due to transition in the magnetic field, $e$ is the charge of an electron, $B$ is the magnetic field, ${m}_{e}$ is the mass of an electron, $c$ is the speed of light, ${m}_{l}$ is the magnetic quantum number, ${E}_{nl}$ is the energy of the electronic energy level in the absence of the magnetic field and $\overline{)h}=\frac{2\mathrm{\pi }}{h}$ where $h$ is the Planck's constant. Zeeman applied this theory to determine the sign of the electronic charge and to estimate the specific charge $\frac{e}{{m}_{e}}$ of the electron, which agreed well with other measurements.The splitting of a spectral line into three components due to a magnetic field as predicted by the quantum theory as also by the Lorentz electron theory is known as the normal Zeeman effect. Actually, the normal Zeeman effect is not commonly observed. In most cases, a spectral line is found to split up into more than three components under the influence of the magnetic field up to several teslas of flux density (i.e., several ten thousand gausses of the magnetic field strength in c.g.s. unit). This type of splitting is known as the anomalous Zeeman effect, which can be explained only when the existence of the electron spin is taken into account.

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