= Solution
{c}
The closed $1s^22s^2$ shells have $L=S=0$, leaving the equivalent $2p^2$ <electrons>. <Addition of angular momentum> and the <Pauli exclusion principle> permit the <atomic terms> ${}^3P,{}^1D,{}^1S$. Their <term symbols> use $^{2S+1}L_J$. <Hund's rules> put the <triplet state> below the <singlet states>; for a less-than-half-filled $p$ shell the smallest $J$ in ${}^3P$ is lowest. Thus
$$
\boxed{\begin{array}{r|c}
(E-E_g)/(hc)\ (\mathrm{cm^{-1}})&1s^22s^22p^2\text{ level}\\\hline
0&{}^3P_0\\
16.4&{}^3P_1\\
43.4&{}^3P_2\\
10192&{}^1D_2\\
21648&{}^1S_0
\end{array}}
$$
All have even <parity>. These assignments agree with independent tabulated <carbon> <energy levels>.<Energy Levels of Neutral Carbon by National Institute of Standards and Technology>[2s²2p² entries: ³P₀,₁,₂ at 0, 16.41671 and 43.41350 cm⁻¹; ¹D₂ at 10192.66 cm⁻¹; ¹S₀ at 21648.02 cm⁻¹]{ref} The rounded source values should not be forced to satisfy an exact <Landé interval rule>; pure first-order <LS coupling> need not account for every measured <fine structure> correction.
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