name and state the rule that explains the presence of 3 unpaired electrons in phosphorus.

Arrangement of electrons in sub-shells of an atom is given by Hund's rule which states that pairing of electrons in the orbitals of same sub-shell will not take place until all the orbitals are singly occupied with parallel spin.
For example: In phosphorus(15), the valence electrons are arranged as follows:

According to the rule, the pairing of electrons in orbitals of 3p doesnot start in P because out of the 5 valence electrons, 2 electrons go to 3s subshell and 3 are singly occupied in 3 orbitals of 3p sub-shell.
Thus, there are 3 unpaired electrons in phosphorus.