The story of the atom begins over two thousand years ago in ancient Greece, when the philosopher Democritus first postulated that matter is made up of fundamental building blocks that cannot be split apart. He called these blocks "atoms", which in ancient Greek meant "indivisible".
Since the times of the ancient Greeks, the model of the atom has been refined over and over again and what we call an atom today is a complex structure that is far from being indivisible.
After the ancient Greeks, quite a long time passed before the next major development in the model of the atom. In 1808, the English scientist John Dalton developed the theory that each chemical element is made of a different kind of atom and that atoms of different elements can combine together to form compounds. Although Dalton had realised that different types of atom existed, he still agreed with Democritus' theory that atoms were indivisible.
It wasn't until another English scientist, Sir Joseph John Thomson, came along in the late 1800s, that a theory where the atom, contrary to its name, was in fact divisible, was first postulated. Thomson's model is known as the "plum pudding model" because Thomson's atom is formed from a mass of positive charge (the "pudding") with negatively charged electrons (the "plums") dispersed throughout it. Although Thomson knew that the electrical charge on an atom was neutral, he did not go so far as to identify any individual positively charged particles within the atom.
The next big step in this story was made in 1911, when Ernest Rutherford performed his famous "Rutherford scattering" experiment. In "Rutherford scattering" alpha particles are emitted from a radioactive source and made to travel towards a very thin sheet of gold foil. Rutherford observed that on reaching the gold foil some alpha particles passed straight though it with a small scattering angle, while other particles were deflected and travelled back towards the source.
From his observations, Rutherford made the important deduction that, in contrast to Thomson's plum pudding model, the electric charge in an atom is not evenly distributed. Rather, Rutherford had discovered that atoms have a concentration of positive charge in their centre. He referred to this concentration of positive charge as the nucleus. He also discovered that this nucleus is surrounded by a sea or cloud of negatively charged particles, or electrons, which orbit the nucleus.
By counting the number of deflected particles and comparing this to the number of particles that passed straight through the foil, Rutherford calculated that the diameter of the nucleus is one ten thousandth of the diameter of the atom. This meant, somewhat surprisingly, that the atom is made up mostly of empty space.
In 1913, not long after Rutherford's important discoveries, a Danish physicist called Niels Bohr atom was worrying about how the electrons actually stayed in their orbits around the nucleus. Classical physics implied that the electrons should gradually lose energy as they orbit and circle inwards towards the nucleus. However, Rutherford had shown that the electrons were in "clouds" around the nucleus and that they remained in their orbits. Bohr then turned to a newly developed field of physics known as quantum mechanics to explain the behaviour of the electrons, as quantum mechanics said that the electrons had to stay in set orbits, or energy levels, around the nucleus, and could only move between these levels in discrete steps or jumps.
After Bohr's contribution, the model of the atom comprised a nucleus containing the protons and electrons in discrete orbits around the nucleus and was looking a lot more like the model of the atom we know today. However, it was still not quite the whole story.
Scientists had measured the mass of atoms and found some to be much heavier than their atomic number (the number of protons) would suggest. Rutherford postulated that a particle called the neutron existed, which had no electrical charge (hence the name neutron) and was contained in the nucleus with the protons. However, it wasn't until 1932 that a physicist called James Chadwick finally discovered the neutron and thus completed our present model of the atom.
Today's model of the atom is accurate and detailed and about as far from the ancient Greek's concept of an indivisible fundamental particle as can be imagined. The journey to reach this model has involved patience, ingenuity, insight, and a number of Nobel Prizes.
However, the story is far from over. After Chadwick's discovery of the neutron, the story passed over to a new group of physicists, the particle physicists, to take up the reins and find out more about the structure of the protons and the neutrons and to explain what holds them together in the nucleus. But that, as they say, is another story.