Liquid nitrogen at its boiling point has density and molar mass (CRC Handbook of…

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

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

Problem

Liquid nitrogen at its boiling point has density

807\,\mathrm{kg\,m^{-3}}

and molar mass

28.01\,\mathrm{g\,mol^{-1}}

(CRC Handbook of Chemistry and Physics). Each

\mathrm{N_2}

molecule has

Z = 14

electrons; take a representative root-mean-square orbital radius of

\langle r^2\rangle^{1/2} = 0.55\,\text{\AA}

per electron (a rough estimate). ((a)) Estimate the diamagnetic volume susceptibility of liquid nitrogen using

\chi_m = -\mu_0N_vZe^2\langle r^2\rangle/6m_e

. ((b)) Converting the CRC Handbook's tabulated molar susceptibility for

\mathrm{N_2}

gas (

-12.0\times10^{-6}\,\mathrm{cm^3\,mol^{-1}}

, cgs) to a volume susceptibility at the liquid's density gives

\chi_m \approx -4.3\times10^{-6}

. Comment on the agreement, and explain why liquid nitrogen behaves so differently from liquid oxygen (

\chi_m \approx +3.5\times10^{-3}

) even though both are diatomic molecular liquids of similar density.