= Solution
{c}
In the idealized isolated-<carbon> <chemical atom> interpretation, both beams carry approximately $2.68\,\mathrm{eV}$ per incident particle, close to the ${}^1S_0$ threshold. However \b[equal incident <energies> do not imply equal excitation channels].
A single optical <photon> cannot strongly excite any of the listed even-<parity> $2p^2$ <energy levels> from the even-<parity> ${}^3P_0$ ground state through an <electric dipole transition>. In particular ${}^3P_0\to{}^1S_0$ also violates $\Delta S=0$ and the $J=0\leftrightarrow0$ restriction. The lowest strong opposite-<parity> excitations lie well above $2.68\,\mathrm{eV}$. Thus one expects no strong resonant <absorption> or corresponding strong atomic fluorescence from these ground-state <chemical atoms> at this optical <wavelength>; weak higher-order processes and scattering are separate effects.
Incident <electrons> can undergo <inelastic scattering> and <collisional excitation>. Their <orbital angular momentum> and exchange with bound <electrons> allow transfers excluded for a single <electric dipole> <photon>. The ${}^1D_2$ <energy level> at $1.264\,\mathrm{eV}$ and the low <fine structure> excitations are energetically accessible. One therefore expects scattered <electrons> with discrete <energy> losses, possible weak forbidden <spectral lines>, and collisional or surface relaxation. For example ${}^1D_2\to{}^3P_2$ has <wavelength> approximately $10^7/(10192-43.4)=985\,\mathrm{nm}$; spin mixing supplies the weak spin-forbidden radiative channel.
There is a numerical threshold caveat. Literally,
$$
E({}^1S_0)=21648hc\,\mathrm{cm^{-1}}\simeq2.68401\,\mathrm{eV},\quad
E_\gamma(462.6\,\mathrm{nm})\simeq2.68016\,\mathrm{eV},\quad E_e=2.68000\,\mathrm{eV}.
$$
Neither quoted beam reaches ${}^1S_0$ from the exact ground state if these are taken as exact monoenergetic values. The <electron> value rounded to two decimal places could represent an actual <energy> above threshold; if so, ${}^1S_0$ is collisionally accessible and its decay to ${}^1D_2$ produces the weak <electric quadrupole transition> at $10^7/11456\simeq873\,\mathrm{nm}$, followed by lower-level relaxation. These emissions require populations and sufficiently low <collisional quenching of a metastable line>.
An actual solid <carbon> foil has bands, collective excitations and surface losses, so it need not reproduce the isolated-<chemical atom> spectrum or selection rules. Its optical and electron-induced emission cannot be predicted quantitatively from the five atomic <energy levels> alone. This is the limitation of the foil wording in the source.
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