GATE 2023 PH – Question 14
The atomic number of an atom is 6. What is the spectroscopic notation of its ground state, according to Hund’s rules?
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Correct answer: (A) $^3P_0$
Explanation
Carbon has atomic number 6, so its ground configuration is $1s^22s^22p^2$. Apply Hund's rules to the two $p$ electrons.
**Rule 1 (maximum $S$):** the two electrons have parallel spins, so $S=1$ and the multiplicity is $2S+1=3$.
**Rule 2 (maximum $L$ for that $S$):** parallel spins require different $m_l$ values. The largest total is $m_l=1+0$, so $L=1$ ($P$ term).
**Rule 3 ($J$):** the $p$ shell has 2 electrons out of 6, which is **less than half full**, so $J$ takes the **smallest** value, $J=|L-S|=0$.
The ground term is $^3P_0$ (option A).