Solution
= Solution
Use the explicit equation $n/n_c=0.002$; the surrounding phrase reverses the verbal ratio. It gives $n_c=2.0\times10^{21}$ cm$^{-3}$. From $\omega_0^2=n_ce^2/(\epsilon_0m_e)$,
$$
\boxed{\lambda=2\pi c\sqrt{\epsilon_0m_e/(n_ce^2)}\simeq0.747\ \mu\mathrm m.}
$$
This is an underdense optical <plasma (physics)>[plasma]. Treating the ratio as $n_c/n=0.002$ would instead contradict the specified underdense condition.