Helium'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

Helium's tabulated polarisability volume is

\alpha/4\pi\varepsilon_0 = 0.21\times10^{-30}\,\mathrm{m^3}

. ((a)) Using the uniform-ball model (

\alpha = 4\pi\varepsilon_0 a^3

), estimate the effective radius

a

of a helium atom and compare it, in one sentence, with the idea that polarisability tracks size rather than atomic mass. ((b)) Estimate the number density

N_v

of helium gas at standard conditions (

T = 273\,\mathrm{K}

P = 1.013\times10^5\,\mathrm{Pa}

) treating it as an ideal gas, and hence estimate the electric susceptibility

\chi_e = N_v\alpha/\varepsilon_0

of the gas. ((c)) Estimate the fractional local-field correction

\chi_e/3

for helium gas at this density, and compare it with the corresponding correction quoted for liquid argon,

0.17

. State which medium the macroscopic field can safely stand in for as the field acting on one molecule.

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