"All atoms having even number of electrons always contain paired electrons"- is the statement true? If so, they by what principle or rule the above statement can be explained?

Explanation

All the electrons, present in atoms with even number of electrons, do not necessarily get paired. This cann be seen from the electronic configuration of carbon (atomic number 6): `1s^(2)2s^(2)2p_(x)^(1)2p_(y)^(1)2p_(z)^(0)`.
In spite of having eve number of electrons (total 6 electrons) the 2p-orbitals of carbon atom have 2 unpaired or odd electrons. this electronic configuration can be explained by Hund's rule. according to this rule-pairing of electrons in the orbital of a particular subshell (degenerate orbitals) does not occur until all the orbitals of that subshell are singly filled up and the singly occupied orbitals must have electrons with parallel spins.