Question

an atom has several subatomic particles, proton, electron and neutron. why the chemist consider an atomic model with three of these particles is sufficient?

Answer 1

The presence of the electrons explains how atoms can become charged, and explains chemical bonding, as the mutual attraction of two charged atomic cores for the same group of "bonding" or "valence" electrons.

The presence of the protons, positively charged, explains how the atom can be electrically neutral if no electrons are missing.

The presence of the neutrons explains how the protons can stick together in the nucleus, even though they repel each other with electric forces. (The even stronger strong nuclear force emitted by the protons and neutrons keep them together).

Additionally, the presence of neutrons explains how some atoms can have almost exactly the same chemical properties (so they have the same number of protons and electrons) -- but weigh differently. (These are called isotopes.) Extra neutrons make an atom weigh more, but don't change (mostly) its chemistry.

There are a host of experiments that directly demonstrate the presence and behaviour of all three particles, and this, plus the explanatory power above, are why we think there are three different subatomic particles in the atom.

Why not more than three? Because no one has found an experimental evidence of a fourth kind of particle, and we don't need a fourth kind of particle to explain any chemical or physical behaviour. Of course, it's always possible someone might discover evidence requiring a fourth subatomic particle tomorrow. Then we'd have to change the model. But we don't think it's super likely, as atoms have been intensely studied for 100 years, and the three-particle model has been sufficient for 70 of those years.