Argon'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 = 1.64\times10^{-30}\,\mathrm{m^3}

, and argon has no permanent dipole moment. Suppose argon gas is compressed at a fixed temperature, so that its number density

N_v

rises from the ideal-gas value of

2.69\times10^{25}\,\mathrm{m^{-3}}

273\,\mathrm{K}

and

1\,\mathrm{atm}

towards the liquid's

2.10\times10^{28}\,\mathrm{m^{-3}}

. ((a)) Show that, in a medium obeying the Clausius-Mossotti relation, the fractional local-field correction

\chi_e/3

equals

y/(1-y)

, with

y=N_v\alpha/3\varepsilon_0

. ((b)) Find the number density at which this correction reaches 5 per cent, and express it as a multiple of the ideal-gas density at

273\,\mathrm{K}

and

1\,\mathrm{atm}

and as a fraction of the liquid density. ((c)) Say what your answer implies about using the macroscopic field in place of the local field for compressed argon gas.

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