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Chapter 8: Problem 11

What is spin-orbit coupling?

Short Answer

Expert verified
Spin-orbit coupling refers to the interaction between the spin and the orbit of an electron, affecting the energy levels of atoms or molecules significantly. It plays a vital role in Quantum Mechanics and is responsible for phenomena like the splitting of atomic energy levels and the fine structure of spectral lines.

Step by step solution

01

Understanding the Concept

Spin-orbit coupling refers to the interaction between the spin of an electron (its inherent angular momentum) and the orbital angular momentum due to its motion around the nucleus. This interaction results from the fact that the magnetic field observed in the electron's rest frame is not solely due to the external field, but also to the magnetic field generated by the motion of the electron in the orbital. The relative alignment of the spin and the orbit can lower or raise the electron's energy, leading to splitting of energy levels.
02

Significance in Quantum Mechanics

In Quantum Mechanics, Spin-Orbit Coupling plays a crucial role as it is responsible for splitting of atomic energy levels, which result in line spectra observed in spectroscopy. It also helps to explain the fine and hyperfine structure of spectral lines and the ground state of the Hydrogen atom when investigated more closely apart from many other phenomena.
03

An Illustrated Example

The electron's spin and orbital angular momenta are usually treated separately, but in some cases, their effects are intertwined. For instance, in the presence of an external magnetic field, the Zeeman effect exhibits splitting of atomic energy levels. This splitting is not solely due to the reaction of the orbital magnetic moment to the external field, but also includes contribution from the electron's spin. This Zeeman effect when including the spin is known as Anomalous Zeeman Effect and highlights the significance of Spin-Orbit Coupling in Quantum Mechanics.

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Most popular questions from this chapter

On what factors does the orbital magnetic dipole moment of an electron depend?

What is the maximum number of orbital angular momentum electron states in the \(n=3\) shell of a hydrogen atom? (Ignore electron spin.)

Explain why spectral lines of the hydrogen atom are split by an external magnetic field. What determines the number and spacing of these lines?

A color television tube generates some X-rays when its electron beam strikes the screen. What is the shortest wavelength of these X-rays, if a 30.0 -kV potential is used to accelerate the electrons? (Note that TVs have shielding to prevent these X-rays from exposing viewers.)

An X-ray tube accelerates an electron with an applied voltage of \(50 \mathrm{kV}\) toward a metal target. (a) What is the shortest-wavelength X-ray radiation generated at the target? (b) Calculate the photon energy in eV. (c) Explain the relationship of the photon energy to the applied voltage.
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