For the diatomic carbon molecule C2 in its ground state, how is it classified magnetically: paramagnetic, diamagnetic, ferromagnetic, or undetermined?

Introduction / Context:
This question tests your understanding of molecular orbital theory and how it is used to predict magnetic properties of diatomic molecules. Magnetism in molecules depends on the presence or absence of unpaired electrons. Paramagnetic substances have one or more unpaired electrons, while diamagnetic substances have all electrons paired. The C2 molecule is a classic example used in examinations to check whether students can correctly fill molecular orbitals and infer magnetic behaviour.

Given Data / Assumptions:
- The species considered is the neutral C2 molecule in its ground state.
- Each carbon atom has atomic number 6, with an electron configuration of 1s2 2s2 2p2.
- We apply basic molecular orbital theory for homonuclear diatomic molecules of second period elements.
- We focus on valence electrons for determining magnetic behaviour.

Concept / Approach:
Magnetic properties depend on unpaired electrons in molecular orbitals. To determine whether C2 is paramagnetic or diamagnetic, we must count the total number of valence electrons and fill molecular orbitals according to their energy ordering, following the Pauli principle and Hunds rule. If all electrons are paired, C2 is diamagnetic; if any are unpaired, it is paramagnetic. For lighter diatomic molecules like B2, C2 and N2, the typical order is sigma 2s, sigma 2s*, pi 2p, sigma 2p, though conventions may differ. The important result is that C2 with 8 valence electrons fills bonding and antibonding orbitals in such a way that all electrons are paired.

Step-by-Step Solution:
Step 1: Determine the total valence electrons in C2. Each carbon atom contributes 4 valence electrons (2s2 2p2), so C2 has 8 valence electrons in total. Step 2: List the relevant molecular orbitals in approximate energy order for lighter homonuclear diatomic molecules: sigma 2s, sigma 2s*, pi 2p, sigma 2p. Step 3: Fill sigma 2s with 2 electrons (paired), then sigma 2s* with 2 electrons (paired), taking up 4 of the 8 valence electrons. Step 4: Place the remaining 4 electrons in the pi 2p orbitals. The two degenerate pi 2p orbitals together can hold 4 electrons. They fill as pairs, giving two pairs of electrons with no unpaired electrons left. Step 5: Confirm that no electrons occupy sigma 2p in the ground state for C2; the 8 valence electrons are already accommodated in lower energy orbitals. Step 6: Since all electrons in the filled molecular orbitals are paired, C2 is diamagnetic.

Verification / Alternative check:
Another way to check is to recall exam standard results for simple diatomic molecules. B2 (10 total electrons, 6 valence) is typically paramagnetic because it has unpaired electrons in pi 2p orbitals. C2 (12 total electrons, 8 valence) is diamagnetic because all valence electrons are paired. N2 (14 total electrons, 10 valence) is also diamagnetic. Remembering this sequence and the corresponding bond orders reinforces that C2 does not have unpaired electrons. Therefore, C2 is diamagnetic in its ground state.

Why Other Options Are Wrong:
Paramagnetic: This would require at least one unpaired electron in a molecular orbital, which is not the case for C2 in the ground state.
Ferromagnetic: Ferromagnetism is associated with bulk materials like iron, not simple diatomic molecules in the gas phase under standard conditions.
Cannot be determined from any theory: Molecular orbital theory does allow us to predict the magnetic nature of C2, so this option is incorrect.

Common Pitfalls:
A common mistake is to misapply the MO energy order for diatomic molecules and incorrectly place electrons in sigma 2p before fully filling pi 2p in the case of lighter elements. This can lead to incorrect predictions about unpaired electrons. Another pitfall is confusing C2 with O2, which is classically paramagnetic. Carefully distinguishing between these species and memorising standard results for B2, C2, N2 and O2 can help avoid these errors.

Final Answer:
The C2 molecule in its ground state is diamagnetic because all its electrons are paired in molecular orbitals.