An unpaired electron is an electron that occupies an atom's orbital single rather than as part of an electron pair.
Each atomic orbital of an atom can hold two electrons with opposing spins.
Because the formation of electron pairs is generally energetically advantageous, whether as a chemical bond or as a lone pair, unpaired electrons are extremely uncommon in chemistry because an entity carrying an unpaired electron is usually quite reactive.
To find the unpaired electrons:
Ag+ represents the d10 system. Because there are no unpaired electrons, the system is diamagnetic.
Mn3+ has the electronic structure [Ar]3d44s0. In 3d, there are four unpaired electrons.
Because of the loss of three electrons, the chromium ion Cr3+ has 24e3e=21e.
