There are two types of forces acting inside a nucleus first the attractive force or the nuclear force that binds the nucleus together along with binding energy and the second one is the repulsive force formed by electrostatic repulsion between the protons in a nucleus.
Now if forces strengths are compared than the electrostatic force is greater than the nuclear force. So, for the atom or nucleus to stay in stable form without approaching decay, the attractive force must be greater than the repulsive force to stop the repulsion in the nucleus.
Now the strength of nuclear forces can’t be increased so the only way to increase nuclear force is to increase the number of neutrons that imparts nuclear force.
Hence, to keep the atom from falling apart the atom needs a greater nuclear force than an electrostatic force and nuclear force can only increase if the number of neutrons is higher than that of protons. Therefore, the numbers of protons are less in stable nuclei than the number of neutrons.
Final Answer: An excess of neutrons which produce only attractive forces, is required for stability.