Solid sodium chloride has density and formula mass

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Magnetic materials · Magnetic materials

The Boundary-Value Problem, Ch Diamagnetism, paramagnetism and magnetic susceptibility

Problem

Solid sodium chloride has density 2170 kg m−32170\,\mathrm{kg\,m^{-3}} and formula mass 58.44 g mol−158.44\,\mathrm{g\,mol^{-1}}, with one Na+\mathrm{Na^+} and one Cl−\mathrm{Cl^-} ion per formula unit (CRC Handbook of Chemistry and Physics). Na+\mathrm{Na^+} has 1010 electrons and Cl−\mathrm{Cl^-} has 1818, so 2828 electrons per formula unit. Take a representative root-mean-square electron radius of ⟨r2⟩1/2=0.40 A˚\langle r^2\rangle^{1/2} = 0.40\,\text{\AA} for the ions in the crystal (a rough estimate based on tabulated ionic radii). ((a)) Estimate the diamagnetic volume susceptibility of solid sodium chloride using χm=−μ0NvZe2⟨r2⟩/6me\chi_m = -\mu_0N_vZe^2\langle r^2\rangle/6m_e, where Z=28Z = 28 is the total number of electrons per formula unit. ((b)) The measured volume susceptibility of sodium chloride is about −1.3×10−5-1.3\times10^{-5}. State whether the estimate has the right sign and order of magnitude, and explain why no paramagnetic term appears to compete with it.

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