Q:

Why are neutrons present in an atom?

I have a very stupid question perhaps, but please answer me. An atom consists of electrons, protons, neutrons. protons are positively charged and electrons are equally negatively charged. The charge of the electrons stabilizes the charge of protons. Why are neutrons present? My question is why physicists believe that neutrons are also present when the charge of electrons and protons can stabilize each other.

A:

In simple terms:
There are four forces governing elementary interactions, their strength and ranges are given in the table.
The strong and the electromagnetic are involved in the nucleus. The other two, weak and gravity are not involved in the formation of a nucleus. Gravity is too weak and the weak interaction is involved in decays only.
The protons are in the nucleus, at the center of the atom, the size of the nucleus is of order of 10^-15 meters. The size of the whole atom is of order 10^-10meters.
Each proton has a positive charge and will repel each other proton. How is it possible that they can stay in one spherical locus called nucleus? The strong force is not strong enough to compensate for the repulsion of two protons. A neutron is attracted to the protons with the strong force and as neutral to first order does not interact with the charge of the proton. This allows it to go close enough so that the strong force gets stronger than the electromagnetic repulsion of another proton. The closer two hadrons get together the stronger the attraction of the strong force. Thus the neutrons shield the positive proton charges from each other and hold the nucleus together. 
You might ask why don't the neutrons form a nucleus? It is because they decay, and outside the balanced forces within a nucleus the probability of decay is very high.  That is why if an isotope has too many neutrons it is liable to beta decay of the neutrons, and if too many protons it is unstable from the electric repulsion of the protons  , though it can pick up an electron and turn a proton to a neutron, and become stable ( electron capture).
The electrons 100.000 times further are  in orbitals and do not repulse each other because there exists a quantum mechanical solution for stable orbitals around the nucleus.
To complete the picture, the state of the nucleus is also a quantum mechanical state, and it has stable energy levels where the protons and neutrons reside, giving up energy to be bound in the nucleus. The difference between the atomic solutions which have orbitals for the electrons comes from the fact that it is the strong force that is dominant in the binding of the nucleons  in the nucleus, and not the electromagnetic.

