# Paramagnetism and Diamagnetism Worked Problem

Here is a worked example problem showing how to tell whether an element is paramagnetic or diamagnetic based on its electron configuration.

### Introduction to Diamagnetism and Paramagnetism

Materials may be classified as ferromagnetic, paramagnetic, or diamagnetic based on their response to an external magnetic field. Ferromagnetism is a large effect, often greater than that of the applied magnetic field, that persists even in the absence of an applied magnetic field.

Diamagnetism is a property that opposes an applied magnetic field, but it's very weak. Paramagnetism is stronger than diamagnetism but weaker than ferromagnetism. Unlike ferromagnetism, paramagnetism does not persist once the external magnetic field is removed because thermal motion randomizes the electron spin orientations.

The strength of paramagnetism is proportional to the strength of the applied magnetic field. Paramagnetism occurs because electron orbits form current loops that produce a magnetic field and contribute a magnetic moment. In paramagnetic materials, the magnetic moments of the electrons don't completely cancel each other out.

All materials are diamagnetic. Diamagnetism occurs when orbital electron motion forms tiny current loops, which produce magnetic fields. When an external magnetic field is applied, the current loops align and oppose the magnetic field. It's an atomic variation of Lenz's law, which states induced magnetic fields oppose the change that formed them.

If the atoms have a net magnetic moment, the resulting paramagnetism overwhelms the diamagnetism. Diamagnetism is also overwhelmed when long range ordering of atomic magnetic moments produces ferromagnetism. So, paramagnetic materials actually are also diamagnetic, but because paramagnetism is stronger, that is how they are classified.

It's worth noting, any conductor exhibits strong diamagnetism in the presence of a changing magnetic field because circulating currents will oppose magnetic field lines. Also, any superconductor is a perfect diamagnet because there is no resistance to formation of current loops.

You can determine whether the net effect in a sample is diamagnetic or paramagnetic by examining the electron configuration of each element. If the electron subshells are completely filled with electrons, the material will be diamagnetic because the magnetic fields cancel each other out. If the electron subshells are incompletely filled, there will be a magnetic moment and the material will be paramagnetic.

### Paramagnetic vs Diamagnetic Examples

Which of the following elements would be expected to be paramagnetic? Diamagnetic?

He, Be, Li, N

### Solution

All of the electrons are spin-paired in diamagnetic elements so their subshells are completed, causing them to be unaffected by magnetic fields. Paramagnetic elements are strongly affected by magnetic fields because their subshells are not completely filled with electrons. So, to determine whether the elements are paramagnetic or diamagnetic, write out the electron configuration for each element.

He: 1s2 subshell is filled

Be: 1s22s2 subshell is filled

Li: 1s22s1 subshell is not filled

N: 1s22s22p3 subshell is not filled