The density of any substance is given by the equation $\text{density, }\rho = \frac{\text{mass, }m\,(kg)}{\text{volume, }V\,(m^{3})}$ or $\rho = \frac{m}{V}$. The typical unit for density is kg m$^{-3}$, however, units such as g cm$^{-3}$ or g litre$^{-1}$ can sometimes be used.
One reason for the high density of gold is that it contains very massive atoms. These atoms are also packed very closely together in a regular arrangement called a crystalline lattice.
Each atom is sitting in a small cubical box of width d, where d is the diameter of each atom.
Measuring the size of atoms
The size of atoms was first measured by Lord Rayleigh in 1890, at a time when many physicists did not believe atoms existed. Rayleigh knew that if oil is split onto water, it will spread out until it can spread no further, as it is then as thin as possible. He realised that at this point the film must be just one atom thick.
Modern measurements of atomic size
In 1915, William Bragg and his son Lawrence received the Nobel Prize for using X-ray diffraction to determine structure, and this included measurements of the separation of atoms.
The development of scanning tunnelling microscopes (STMs) in the 1980s made direct observation of atoms possible.
The magnification of the STM is known, so direct measurement on an image reveals, for example, that a copper atom has a diameter of 0.25 nm.