= Solution
The supplied <density> is $4\times10^{24}$ m$^{-3}$. Therefore
$$
\boxed{\omega_p\simeq1.13\times10^{14}\ \mathrm{s^{-1}},\quad \lambda_p=2\pi c/\omega_p\simeq16.7\ \mu\mathrm m.}
$$
The cold relativistic field scale is $E_0=m_ec\omega_p/e\simeq1.92\times10^{11}$ V m$^{-1}$, corresponding to an <energy> <gradient> $\boxed{eE_0\simeq192\ \mathrm{GeV\,m^{-1}}}$. It is an upper scale for the stipulated large-amplitude <wave>, not proof that the particular weak driver produces that field.
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