Final answer:
No, a molecule with an odd number of electrons cannot be diamagnetic because it must have at least one unpaired electron making it paramagnetic. The correct option is b).
Step-by-step explanation:
The question pertains to whether a molecule with an odd number of electrons can ever be diamagnetic. The answer is no, it cannot.
According to molecular orbital theory, a molecule with an odd number of electrons must have at least one unpaired electron, because electrons pair up in orbitals, and an odd number means there will be an imbalance with one leftover electron.
In more detail, electrons fill molecular orbitals following the rules outlined by Hund's rule and the Aufbau principle. Energy levels fill starting from the lowest going upwards, and only a maximum of two electrons can occupy a single orbital with opposite spins.
When there is an odd number of electrons, at least one electron will be without a partner to pair with. This unpaired electron makes the molecule paramagnetic, which means it is attracted to a magnetic field.
Diamagnetism, on the other hand, occurs when all the electrons in a molecule are paired, which results in the molecule being repelled by a magnetic field. Option b) is the correct one.