Which sequence represents a correct order of historical developments leading to the modern model of the atom?

(1) the atom is a hard sphere = >most of the atom is empty space=> electrons exist in orbitals outside the nucleus

(2) the atom is a hard sphere = > electrons exist in orbitals outside the nucleus = > most of the atom is empty space

(3) most of the atom is empty space = >electrons exist in orbitals outside the nucleus = > the atom is a hard sphere

(4) most of the atom is empty space=>the atom is a hard sphere = > electrons exist in orbitals outside the nucleus

The correct order is shown by the first option:

(1) the atom is a hard sphere → most of the atom is empty space → electrons exist in orbitals outside the nucleus

Explanation:

1) the atom is a hard sphere

This was the original conception of the atom.

The plum pudding model, developed by the scientist, J. J. Thompson, by 1904, after the discovery of the electron, represented the atom as a solid positively charged sphere with electrons embeded and uniformly distributed in it.

2) most of the atom is empty space

It corresponds to the model developed by Rutherford, by 1911.

The famous experiment of α-particles bombarding a thin foil of gold, yield to the discovery of the atomic nucleous and the proposition that the mass of the atom is mostly concentrated in a dense small positevely charged nucleous with electrons (negative charged) around of it and a lot of empty space in between the electrons and the nucleous. This model did not explain how the electrons were arranged.

3) electrons exist in orbitals outside the nucleus.

Few years later, by 1913, the scientist Niels Bhor, proposed the model in which the electrons were in fixed orbits around the nucleous, just like the planets orbit around the sun, to explain the emission spectra of the atoms.

This was not the last theory. It was not exact and a new atom quantum model was soon developed, but this is not part of the question.

The answer is (1). Democritus's model came first, then Rutherford's model. Bohr's subsequent model built upon Rutherford's, confining electrons to specified orbits around the nucleus.