Spin magnetic moment

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1 Basis for spin magnetic moments
2 Calculation
3 Spin in chemistry
4 History of spin magnetic moments
5 Sources
6 External links

[edit] Basis for spin magnetic moments

A spin magnetic moment is induced by all charged particles, but the particle most usable by modern technology is a certain lepton, the electron. Specifically, a spin magnetic moment is created because a particle has a physical property known as spin and electric charge. The spin within classical physics would be an object that rotates axially around its center of mass. In quantum mechanics, elementary particles are points, which have no axis to revolve around. This means these particles do not have spin in a classical sense, as angular momentum is defined by $\mathbf{L} = \mathbf{r} \times \mathbf{p}$ , but have the physical property of angular momentum (see Spin (physics)). Maxwell's theory of magnetic fields dictates that any moving charged particle creates a magnetic moment, and by definition, angular momentum designates movement. This is where the magnetic moment emerges in classical electromagnetism. See Maxwell's equation

[edit] Calculation

We can find a spin magnetic moment for a particle with charge $q$ , mass $m$ , and spin S by calculating:

$\vec{\mu}_S \ = \ g \ \frac{q}{2 m} \ \vec{S}$

where $g$ is a dimentionless number, called the g-factor. This number depends on the particle: it is about $g = 2$ for the electron, $g = 5.586$ for the proton, and $g = - 3.826$ for the neutron. The proton and neutron are composed of quarks, which have a non-zero charge and a spin of $\hbar/2$ , and this must be taken into account when calculating their g-factors. Even though the neutron has a charge $q = 0$ , its quarks give it a magnetic moment. The proton and electron's spin magnetic moments can be calculated by simply setting $q = e$ .

The electron's spin magnetic moment is approximately equal to the Bohr magneton because $g\approx 2$ and the electron's spin is $s = 1 / 2$ :

$\mu_S\approx 2\frac{e}{2m_e}\frac{\hbar}{2}=\mu_B$ .

[edit] Spin in chemistry

Spin magnetic moments create a basis for one of the most important principles in chemistry, the Pauli exclusion principle. This principle, first suggested by Wolfgang Pauli, governs most of modern-day chemistry. The theory plays further roles than just the explanations of doublets within electromagnetic spectrum. This additional quantum number, spin, became the basis for the modern standard model used today, which includes the use of Hund's rules, and an explanation of beta decay.

[edit] History of spin magnetic moments

Wolfgang Pauli first suggested the motion of spin magnetic moments after reviewing an experiment with sodium. The experiment showed that under high resolution the sodium atom emitted a doublet in the electromagnetic spectrum of wavelength 589 nanometers and 589.6 nanometers. The experiment was performed in 1925 and no experimental models of the time could predict such empirical data. Therefore, with the help of George Uhlenbeck and Samuel Goudsmit, Wolfgang Pauli proposed a new quantum number known as spin.

[edit] Sources

Raymond A. Serway; & John W. Jewett, Principles of Physics (A calculus based version 4th addition). Printed in Canada Thomson Learning ISBN 0-534-49143-X.