Suscept. of a Diamagnet (eqn): what are these variables?

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SUMMARY

The discussion focuses on the susceptibility of a diamagnet, specifically analyzing the equation χ_m = - (Z e² n μ₀) / (4 m) . The variable n represents the electron density, defined as n = N/V, where V is the volume of a unit cell containing Z electrons, leading to n = 1/a³. The mass m in the denominator is clarified to be the mass of the electron, not the proton, which is crucial for accurate calculations of diamagnetic susceptibility.

PREREQUISITES
  • Understanding of diamagnetism and magnetic susceptibility
  • Familiarity with quantum mechanics and wave functions
  • Knowledge of atomic structure, specifically hydrogen atom properties
  • Basic grasp of solid-state physics and unit cell concepts
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  • Study the derivation of diamagnetic susceptibility equations
  • Learn about the role of electron density in solid-state physics
  • Explore the concept of Larmor frequency in quantum mechanics
  • Investigate the properties of wave functions in quantum systems
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Students and researchers in physics, particularly those studying quantum mechanics, solid-state physics, and materials science, will benefit from this discussion.

bhimberg
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[tex]\chi_m = - \frac{Z e^2 n \mu_0}{4 m} <p^2>[/tex]

My understanding is that [tex]n = N/V[/tex], where the volume is the volume of a unit cell containing Z electrons (in this case [tex]n = \frac{1}{a^3}[/tex]). The m in the denominator is related to the larmor frequency and, for a hydrogen atom, should be the mass of a proton.

[tex]<p^2>[/tex] is an expectation value of the wave function of the hydrogen atom. While this is certainly a homework question, I'm asking for general guidance about the equation. Am I correct in assuming [tex]m = m_p[/tex] is the mass of a proton? My numbers keep coming out many orders of magnitude greater so I must be missing something fundamental.
 
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