= Solution
For statistically independent <Thomson scattering> events, the probability of no scattering over a proper distance $s$ is $\exp(-n_e\sigma_e s)$. The <photon mean free path in an ionized universe> is therefore
$$
\boxed{
\ell_\gamma=\frac1{n_e\sigma_e}
=\frac1{(2\times10^{17})(6.7\times10^{-29})}
\simeq7.5\times10^{10}\,\mathrm m.
}
$$
This is about half an <astronomical unit>. It is a proper distance at that epoch, not a present-day comoving distance. The <Thomson scattering> approximation is appropriate because the electrons are nonrelativistic and typical photon energies are much smaller than $m_ec^2$. The source's spelling of the process is a typographical error; the physical process is Thomson scattering.
Back to article page
