Solution
= Solution
For this <equal-mass Coulomb circular orbit>, let $s$ be the separation and $k_e=1/(4\pi\epsilon_0)$. Each particle describes a circle of radius $s/2$ about the <centre of mass>. <Coulomb's law> and <centripetal acceleration> give
$$
\frac{k_ee^2}{s^2}=m_e\omega^2\frac s2,
\qquad
\boxed{T=2\pi\sqrt{\frac{m_es^3}{2k_ee^2}}=2.79\times10^{-10}\,\mathrm s.}
$$
Using $s$ as each particle's orbital radius would miss the equal-mass two-body motion.