Neon's tabulated polarisability volume is

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electric fields in matter · Electric fields in matter

The Boundary-Value Problem, Ch Molecular polarisability, permanent dipoles and the Clausius-Mossotti relation

Problem

\alpha/4\pi\varepsilon_0 = 0.396\times10^{-30}\,\mathrm{m^3}

. Liquid neon at its boiling point has density

1.207\times10^3\,\mathrm{kg\,m^{-3}}

and molar mass

20.18\times10^{-3}\,\mathrm{kg\,mol^{-1}}

; neon has no permanent dipole moment. The measured relative permittivity of the liquid is

1.20

. Take

N_A = 6.022\times10^{23}\,\mathrm{mol^{-1}}

. ((a)) Find the effective radius

a

of a neon atom from its polarisability volume. ((b)) Find the number density

N_v

of atoms in the liquid. ((c)) Predict

\varepsilon_r

using the Clausius-Mossotti relation and compare with the measured value.