To understand the magnetic nature of a molecule like fluorine (\(\text{F}_2\)), one must delve into the quantum mechanical arrangement of its electrons. Molecular magnetism is determined by how a substance interacts with a magnetic field. Predicting whether \(\text{F}_2\) is attracted to or repelled by a magnet requires examining its electronic structure.
The Difference Between Diamagnetism and Paramagnetism
The magnetic behavior of any material is determined by the spin of its electrons, which act like tiny individual magnets. Substances fall into two primary categories based on this behavior when placed near an external magnetic field: diamagnetic or paramagnetic. The distinction rests entirely on whether the electrons within the molecule are paired or unpaired.
A substance is classified as diamagnetic if all of its electrons are paired up in their respective orbitals. In this configuration, the magnetic moment of each electron is perfectly canceled by its partner spinning in the opposite direction. The molecule has no permanent magnetic moment, causing it to be weakly repelled by an external magnetic field.
Conversely, a substance is considered paramagnetic if it possesses one or more unpaired electrons. Each unpaired electron contributes a net magnetic moment to the molecule, which aligns itself with an external magnetic field. This alignment results in the molecule being weakly attracted toward the source of the magnetic field.
Molecular Orbital Theory: The Predictive Tool
Traditional bonding models, such as Lewis structures, often fail to accurately predict a molecule’s magnetic properties. For example, simple models incorrectly classify the oxygen molecule (\(\text{O}_2\)) as diamagnetic, even though experimental evidence clearly shows oxygen is paramagnetic.
Molecular Orbital Theory (MOT) provides the necessary quantum mechanical framework to correctly determine the electronic structure of molecules. MOT posits that when atoms combine, their atomic orbitals merge to form new molecular orbitals that span the entire molecule. These resulting molecular orbitals are categorized as bonding (lower energy, stabilizing) or antibonding (higher energy, destabilizing).
The combination of atomic orbitals yields sigma (\(\sigma\)) orbitals, with electron density along the internuclear axis, and pi (\(\pi\)) orbitals, with density above and below the axis. Electrons systematically fill these molecular orbitals starting with the lowest energy level. The Pauli exclusion principle dictates that each orbital holds a maximum of two electrons with opposite spins.
When filling degenerate (equal energy) orbitals, Hund’s rule requires electrons to occupy each orbital singly before pairing occurs. By rigorously applying these principles to the total number of valence electrons, MOT definitively predicts the presence or absence of unpaired electrons, making it indispensable for magnetic classification.
Orbital Filling and the Magnetic State of \(\text{F}_2\)
The fluorine molecule (\(\text{F}_2\)) is formed from two fluorine atoms, each contributing seven valence electrons. This gives \(\text{F}_2\) a total of 14 valence electrons to be distributed among the molecular orbitals.
The lowest energy valence orbitals are the \(\sigma_{2s}\) and the antibonding \(\sigma^{}_{2s}\). The first four valence electrons fill these two orbitals completely, resulting in four paired electrons.
The remaining ten valence electrons populate the orbitals derived from the \(2p\) atomic orbitals. For \(\text{F}_2\), the next lowest energy orbital is the bonding \(\sigma_{2p}\), which accommodates two electrons. The remaining eight electrons then fill the two degenerate \(\pi_{2p}\) bonding orbitals, followed by the two degenerate \(\pi^{}_{2p}\) antibonding orbitals.
Once all 14 valence electrons are placed, the resulting electron configuration shows that every electron is paired within its orbital. The \(\sigma_{2p}\), the two \(\pi_{2p}\) orbitals, and the two \(\pi^{}_{2p}\) orbitals are all completely full. Since there are zero unpaired electrons in the \(\text{F}_2\) molecule, Molecular Orbital Theory concludes that \(\text{F}_2\) is diamagnetic.
How Molecular Magnetic Properties Are Measured
The theoretical prediction that \(\text{F}_2\) is diamagnetic is confirmed through physical measurement in a laboratory setting. The most common technique for determining a substance’s magnetic susceptibility is the Gouy balance method. This technique measures the force exerted on a sample when it is placed within a non-uniform magnetic field.
In a Gouy balance experiment, a cylindrical tube containing the molecular substance is suspended from a sensitive balance, with one end positioned between the poles of a strong electromagnet. When the magnetic field is turned on, a change in the sample’s apparent weight is observed.
A paramagnetic substance is attracted to the field, experiencing a downward pull that results in an apparent increase in weight. Conversely, a diamagnetic substance like \(\text{F}_2\) is repelled by the magnetic field, experiencing a slight upward push. This upward force causes an apparent decrease in the sample’s weight when the field is applied. By accurately measuring this small change, scientists can quantify the magnetic susceptibility and confirm the absence of unpaired electrons, validating the theoretical prediction.