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.
A: We "know" that the neutrons are in the nucleus because they add to the weight of the atom. This is particularly visible in the case of isotopes. If you have some 12C (carbon with 6 protons and 6 neutrons in the nucleus) and some 13C (carbon with 6 protons and 7 neutrons in the nucleus), then both are definitely "carbon" (they engage in the same kind of reaction) so they have the same number of electrons, hence the same number of positive charges in the nucleus (since an atom is electrically neutral); but the 13C is definitely heavier (by about 8.3%). Thus, there must be some extra component in the nucleus, that does not add to the charge but has a definite mass.
Historically, the discovery of the neutron came first from an experiment from Rutherford, who was throwing alpha particles (helium nuclei) at a gold foil, and measuring how the particles were scattered. The scattering required that the gold nucleus was substantially heavier than the mass of its protons.
Later on we got a lot more data on neutrons, allowing us to not only be quite certain of their presence, but also measure a lot of their properties.

Within the nucleus, protons and neutrons stick together. The protons, being all positively charged, would very much like to fly apart from each other; but they are bound by the strong interaction which is much stronger than the electromagnetic repulsion (but with a very short range). That force also works on neutrons, which is why they stick (though, having a neutral charge, they are not so eager to leave).
A neutron, by itself, is not stable. It is slightly heavier than a proton, and, left alone, decays into a proton+electron after a few minutes (and an antineutrino). Within a stable nucleus, neutrons cannot decay because there is no room for an extra proton with the quantum state that would result from such a decay. When the nucleus has too many neutrons with regards to its number of protons, it is not stable, meaning that a neutron can morph into a proton, emitting an electron in the process (this is called beta decay).
Thus, neutrons stick to the nucleus because of the strong interaction, and they stay there indefinitely because the nucleus structure stabilizes them, preventing them from decaying.
