Helium gas, used to fill balloons and as a laser and shielding gas, has a measured…

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Wave propagation and light in media · Wave propagation and light in media

Optics and Photonics, Ch Light as an electromagnetic wave in matter

Problem

Helium gas, used to fill balloons and as a laser and shielding gas, has a measured density

\rho = 0.166\ \mathrm{kg\,m^{-3}}

at room temperature and atmospheric pressure, and a molar mass

M = 4.00\ \mathrm{g\,mol^{-1}}

. Avogadro's constant is

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

. As the text does for air, model each helium atom as contributing one effective oscillating electron, bound with a single resonance frequency corresponding to the atom's strongest ultraviolet absorption line, guessed here at

\lambda_0 = 58.4\ \mathrm{nm}

. ((a)) Find the number density

\mathcal{N}

of helium atoms from its density and molar mass. ((b)) Use the dilute-gas Lorentz formula to estimate

n - 1

for visible light of vacuum wavelength

589\ \mathrm{nm}

(the sodium D line), first checking that

\omega \ll \omega_0

so the

\omega^2

term may be dropped. ((c)) The tabulated refractive index of helium at this wavelength and these conditions is

n - 1 = 3.50\times10^{-5}

. Compare your estimate with this value and comment briefly on the size of any discrepancy.

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