A crystal of \(\mathrm{Fe}_{3} \mathrm{O}_{4}\) is: (a) Diamagnetic (b) Ferromagnetic (c) Paramagnetic (d) None of these

When we talk about ferromagnetism, we're describing a strong form of magnetism that's associated with materials like iron, nickel, and cobalt. These materials can become permanently magnetized.

What's special about these materials is that their atoms have magnetic moments—essentially tiny magnets—due to unpaired electrons. In ferromagnetic materials, these magnetic moments align parallel to each other within regions called domains. When the material is magnetized, the domains line up in the same direction, resulting in a strong cumulative magnetic field. With the case of iron oxides like (Fe_3O_4), this alignment is what gives it ferromagnetic properties, making it strongly attracted to magnetic fields and capable of retaining magnetization.

Paramagnetism is a weaker form of magnetism exhibited by certain materials, including aluminum and oxygen, which become magnetic only in the presence of an external magnetic field.

It occurs in substances where there are unpaired electrons, and each unpaired electron has a magnetic dipole moment. Unlike ferromagnets, these do not maintain their magnetization in the absence of an external field as thermal motion randomizes the spin orientations. In iron oxides, both (Fe^{2+}) and (Fe^{3+}) ions exhibit unpaired electrons, contributing to its overall magnetic nature.

Diamagnetism is present in all materials and is characterized by a very weak and negative susceptibility to magnetic fields. This means that diamagnetic materials are repelled by a magnetic field.

Interestingly, the electrons in diamagnetic materials are all paired up, and paired electrons tend to cancel out each other's magnetic field. So, in ideal diamagnetism, there are no unpaired electrons, leading to no net magnetic moment. However, when a magnetic field is applied, these materials create an induced magnetic field in the opposite direction, which is why they are repelled. An example of a diamagnetic material is bismuth.

At the heart of understanding magnetic properties of substances is electron configuration. Electrons in an atom are organized into shells and subshells, and each can hold a certain number of electrons based on the rules of quantum mechanics.

In terms of magnetism, it's particularly important to consider the outermost electrons as they determine how individual atoms interact with each other. Unpaired electrons, which can be identified by looking at electron configurations, are essential for magnetism. Whether electrons are paired or unpaired will tell us if the substance is diamagnetic (paired) or paramagnetic (unpaired). In the case of iron oxide (Fe_3O_4), the unpaired electrons in the iron ions lead to its overall magnetic character.