Question

The magnetic character of bulk matter is determined largely by electron spin magnetic moments, rather than by orbital dipole moments. (Nuclear contributions are negligible, as the proton's spin magnetic moment is about 658 times smaller than that of the electron.) If the atoms or molecules of a substance have unpaired electron spins, the associated magnetic moments give rise to paramagnetic behavior or to ferromagnetic behavior if the interactions between atoms or molecules are strong enough to align them in domains. If the atoms or molecules have no net unpaired spins, then magnetic perturbations of the electron orbits give rise to diamagnetic behavior. a) Molecular hydrogen gas $\left({\mathrm{H}}_2\right)$ is weakly diamagnetic. What does this imply about the spins of the two electrons in the hydrogen molecule? b) What would you expect the magnetic behavior of atomic hydrogen gas (H) to be?

Short answer

Answer: In H₂, weak diamagnetism implies that the two electrons have paired (opposite) spins, leading to no net unpaired electron spin and resulting in diamagnetic behavior. On the other hand, atomic hydrogen gas (H) is expected to exhibit paramagnetic behavior due to the presence of an unpaired electron spin.

Step-by-step solution

a) Implications of weak diamagnetism on electron spins in H₂

Molecular hydrogen gas (H₂) is weakly diamagnetic, which means the electrons in the molecule do not possess any net unpaired spins and the presence of an external magnetic field makes it repel slightly. In H₂, there are two electrons, and weak diamagnetism implies that these two electrons have paired (opposite) spins. When the spins are paired, their magnetic moments cancel each other out, leading to no net unpaired electron spin and resulting in diamagnetic behavior.

b) Predicting the magnetic behavior of atomic hydrogen gas (H)

Atomic hydrogen gas (H) has one electron in its outer shell. Since there is only one electron, it has an unpaired spin. An unpaired electron spin means that the magnetic moment is not canceled out, as there is no pairing with another electron. In such a scenario, the material exhibits paramagnetic behavior. Therefore, we can expect atomic hydrogen gas (H) to exhibit paramagnetic behavior due to the presence of an unpaired electron spin.

Key concepts

Electron Spins

Electron spins play a crucial role in the magnetic properties of atoms and molecules. Electrons possess a property called "spin," which can be thought of as them having a tiny magnetic moment. This magnetic moment can align in different ways and is a fundamental factor in determining the magnetism of a material.

When studying a substance's magnetic properties, it's vital to consider how its electrons are spinning:

• **Paired Spins:** When electrons are paired, one electron's spin is opposite to the other, canceling their magnetic moments out. As a result, the substance exhibits no net magnetism from these paired spins.
• **Unpaired Spins:** In situations where there are unpaired electrons, their spins do not cancel out. This results in a net magnetic moment, meaning the material may show magnetic behavior.

This concept of electron spins is crucial when predicting whether a substance will show properties of paramagnetism or diamagnetism.

Paramagnetism

Paramagnetism is a form of magnetism that materials exhibit due to the presence of unpaired electron spins. These unpaired electrons create a net magnetic moment because their spins do not cancel each other out. This characteristic often leads to a weak attraction to an external magnetic field.

There are a few key points that help us understand paramagnetic materials:

• **Unpaired Electrons:** The presence of one or more unpaired electrons is what gives rise to paramagnetism. As in the case of atomic hydrogen, these unpaired spins lead to a net magnetic moment.
• **Temperature Dependence:** Paramagnetic behavior tends to decrease with rising temperature because thermal agitation can disrupt the alignment of magnetic moments.

Due to the random orientation of these spins in the absence of a magnetic field, paramagnetic materials do not retain magnetization, unlike ferromagnetic materials, which can hold magnetization even without an applied field.

Diamagnetism

Diamagnetism is a type of magnetism that occurs in materials like molecular hydrogen ( H_2 ), where all electron spins are paired, resulting in no net magnetic moment. When exposed to an external magnetic field, diamagnetic substances exhibit a slight repulsion. This is due to changes in electron orbits caused by the magnetic field.

Key characteristics of diamagnetism include:

• **Paired Electron Spins:** As all the electron spins in diamagnetic materials are paired, their magnetic moments cancel out, leading to no net magnetic effect.
• **Universal Property:** Diamagnetism is a property of all materials, but it's usually overshadowed by stronger magnetic effects, such as paramagnetism, when unpaired electrons are present.

Diamagnetic behavior is very subtle, often only noticeable in materials without any unpaired spins or in the presence of a very strong magnetic field. This is why molecular hydrogen, with both electron spins paired, exhibits weak diamagnetism.