A lithium atom has three electrons, and the S1 / 2 ground- state electron configuration is 1s^

step 1 So the energy of the photon in the first transition, E1, which is the 2p3 halves to the 2S1 half

A lithium atom has three electrons, and the S1 / 2 ground- ...

A lithium atom has three electrons, and the $S_{1 / 2 \text { ground- }}$ state electron configuration is 1$s^{2} 2 s .$ The 1$s^{2} 2 p$ excited state is split into two closely spaced levels, $^{2} P_{3 / 2}$ and $^{2} P_{1 / 2},$ by the spin-orbit interaction (see Example 41.7 in Section 41.5$) .$ A photon with wavelength 67.09608$\mu \mathrm{m}$ is emitted in the $^{2} P_{3 / 2} \rightarrow^{2} S_{1 / 2}$ transition, and a photon with wavelength 67.09761$\mu \mathrm{m}$ is emitted in the 2$P_{1 / 2} \rightarrow^{2} S_{1 / 2}$ transition. Calculate the effective magnetic field seen by the electron in the 1$s^{2} 2 p$ state of the lithium atom. How does your result compare to that for the 3$p$ level of sodium found in Example 41.7$?$

A lithium atom has three electrons, and the $S_{1 / 2 \text { ground- }}$ state electron configuration is 1$s^{2} 2 s .$ The 1$s^{2} 2 p$ excited state is split into two closely spaced levels, $^{2} P_{3 / 2}$ and $^{2} P_{1 / 2},$ by the spin-orbit interaction (see Example 41.7 in Section 41.5$) .$ A photon with
wavelength 67.09608$\mu \mathrm{m}$ is emitted in the $^{2} P_{3 / 2} \rightarrow^{2} S_{1 / 2}$ transition, and a photon with wavelength 67.09761$\mu \mathrm{m}$ is emitted in the 2$P_{1 / 2} \rightarrow^{2} S_{1 / 2}$ transition. Calculate the effective magnetic field seen by the electron in the 1$s^{2} 2 p$ state of the lithium atom. How does your result compare to that for the 3$p$ level of sodium found in Example 41.7$?$

Key Concepts

Spectroscopic Transitions and Photon Emission

Spectroscopic transitions involve electrons moving between energy levels, resulting in the emission or absorption of photons. By analyzing the wavelengths of the emitted photons, one can determine the energy differences between states and thus infer physical quantities like the effective magnetic field associated with spin-orbit splitting.

Effective Magnetic Field

The effective magnetic field is a conceptual tool that translates the impact of spin–orbit interaction into an equivalent magnetic field experienced by the electron. By relating the energy splitting (due to spin–orbit coupling) to the magnetic moment of the electron, one can deduce an effective field strength that characterizes this interaction.

Spin-Orbit Coupling

Spin–orbit coupling is the interaction between an electron's intrinsic spin and its orbital motion around the nucleus. This interaction causes energy levels that would otherwise be degenerate to split into slightly different energies, a fundamental mechanism behind the fine structure observed in atomic spectra.

Electron Configuration

Electron configuration describes the arrangement of electrons in the various atomic orbitals, determining the atom’s ground and excited states. In atoms like lithium, the configuration explains why certain electrons participate in transitions that lead to observable spectroscopic effects.

Fine Structure Splitting

Fine structure splitting refers to the small energy differences between closely spaced atomic levels. It originates largely from relativistic corrections and spin–orbit coupling, and its magnitude can be measured through the slight differences in transition wavelengths between energy levels.

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