## Diamagnetism and Paramagnetism

#### Learning Objective

• Distinguish diamagnetic from paramagnetic atoms.

#### Key Points

• Any time two electrons share the same orbital, their spin quantum numbers have to be different. Whenever two electrons are paired together in an orbital, or their total spin is 0, they are diamagnetic electrons. Atoms with all diamagnetic electrons are called diamagnetic atoms.
• A paramagnetic electron is an unpaired electron. An atom is considered paramagnetic if even one orbital has a net spin. An atom could have ten diamagnetic electrons, but as long as it also has one paramagnetic electron, it is still considered a paramagnetic atom.
• Diamagnetic atoms repel magnetic fields. The unpaired electrons of paramagnetic atoms realign in response to external magnetic fields and are therefore attracted. Paramagnets do not retain magnetization in the absence of a magnetic field, because thermal energy randomizes electron spin orientations.

#### Terms

• paramagneticMaterials that are attracted by an externally applied magnetic field and form internal, induced magnetic fields in the direction of the applied magnetic field.
• diamagneticMaterials that create an induced magnetic field in a direction opposite to an externally applied magnetic field and are therefore repelled by the applied magnetic field.
• lanthanideAny of the 14 rare earth elements from cerium (or from lanthanum) to lutetium in the periodic table. Because their outermost orbitals are empty, they have very similar chemistry. Below them are the actinides.
• quantum numberOne of certain integers or half-integers that specify the state of a quantum mechanical system (such as an electron in an atom).
• MRIMagnetic Resonance Imaging, a medical imaging technique used in radiology to investigate the anatomy and physiology of the body in both health and disease.

## Diamagnetism

Any time two electrons share the same orbital, their spin quantum numbers have to be different. In other words, one of the electrons has to be “spin-up,” with $m_s = +\frac{1}{2}$, while the other electron is “spin-down,” with $m_s = -\frac{1}{2}$. This is important when it comes to determining the total spin in an electron orbital. In order to decide whether electron spins cancel, add their spin quantum numbers together. Whenever two electrons are paired together in an orbital, or their total spin is 0, they are called diamagnetic electrons.

Think of spins as clockwise and counterclockwise. If one spin is clockwise and the other is counterclockwise, then the two spin directions balance each other out and there is no leftover rotation. Note what all of this means in terms of electrons sharing an orbital: Since electrons in the same orbital always have opposite values for their spin quantum numbers (ms), they will always end up canceling each other out. In other words, there is no leftover spin in an orbital that contains two electrons.

Electron spin is very important in determining the magnetic properties of an atom. If all of the electrons in an atom are paired up and share their orbital with another electron, then the total spin in each orbital is zero and the atom is diamagnetic. Diamagnetic atoms are not attracted to a magnetic field, but rather are slightly repelled.

## Paramagnetism

Electrons that are alone in an orbital are called paramagnetic electrons. Remember that if an electron is alone in an orbital, the orbital has a net spin, because the spin of the lone electron does not get canceled out. If even one orbital has a net spin, the entire atom will have a net spin. Therefore, an atom is considered to be paramagnetic when it contains at least one paramagnetic electron. In other words, an atom could have 10 paired (diamagnetic) electrons, but as long as it also has one unpaired (paramagnetic) electron, it is still considered a paramagnetic atom.

Just as diamagnetic atoms are slightly repelled from a magnetic field, paramagnetic atoms are slightly attracted to a magnetic field. Paramagnetic properties are due to the realignment of the electron paths caused by the external magnetic field. Paramagnets do not retain any magnetization in the absence of an externally applied magnetic field, because thermal motion randomizes the spin orientations. Stronger magnetic effects are typically only observed when d- or f-electrons are involved. The size of the magnetic moment on a lanthanide atom can be quite large, as it can carry up to seven unpaired electrons, in the case of gadolinium(III) (hence its use in MRI).