Which of the following best describes the magnetic properties of the molecule B_2, and why?

• A. B_2 is diamagnetic because it contains only s electrons.
• B. B_2 is diamagnetic because all of its electrons are paired in its molecular orbitals.
• C. B_2 is paramagnetic because it has a completely filled valence shell.
• D. B_2 is paramagnetic because it has unpaired electrons in its molecular orbitals.

Answer: (D)

Verified step by step guidance

1. Recall that the magnetic properties of a molecule depend on the presence of unpaired electrons: molecules with unpaired electrons are paramagnetic, while those with all paired electrons are diamagnetic.
2. Determine the total number of valence electrons in the B_2 molecule. Since each boron atom has 3 valence electrons, B_2 has a total of 6 valence electrons.
3. Use the molecular orbital (MO) diagram for B_2 to fill the electrons into the molecular orbitals in order of increasing energy. For B_2, the order of orbitals is typically: \(\sigma_{2s}\), \(\sigma_{2s}^*\), \(\pi_{2p_x} = \pi_{2p_y}\), \(\sigma_{2p_z}\).
4. Fill the 6 valence electrons into the MOs following Hund's rule and the Pauli exclusion principle. This will show that there are unpaired electrons in the \(\pi_{2p}\) orbitals.
5. Conclude that because B_2 has unpaired electrons in its molecular orbitals, it exhibits paramagnetism, which explains why the correct description is that B_2 is paramagnetic due to unpaired electrons.