Question

How do you calculate atomic volume?

Answer 1

Hint: Atomic volume is a measure of the space occupied by matter (subatomic) particles inside an atom and therefore one needs values of other physical quantities like atomic mass and density of the atom to calculate atomic volume.

Complete answer:
According to Dalton’s Atomic theory, an atom is the smallest building block of matter around us. Various theories and studies of atomic structure indicate that it consists of subatomic particles like protons, neutrons and electrons. No matter how small these particles are, they are known to possess some mass and occupy certain space that constitutes the atomic volume.
Atomic volume can be defined as the total space acquired by one mole of an element in its solid form. It can be calculated by finding out the ratio between the gram atomic weight and the density of the concerned element in solid state.
$$\text{Atomic volume}={\displaystyle \frac{\text{gram atomic weight}}{\text{density of atom in solid form}}}c{m}^{3}mo{l}^{-1}$$
Though in most cases we assume all atoms to be perfectly spherical in nature, most atoms tend to exist with distorted electrons clouds or limited symmetry. This makes it difficult to calculate the volume of each individual atom by using their atomic radii to calculate their spherical volumes.
But advanced techniques like XRD have been developed that help determine the approximate bond distances of elements in their solid state through crystallographic methods. Upon doing so we can calculate the atomic radius $${}^{\prime }{r}^{\prime }$$. Thus atomic volume of an individual atom can be calculated using the following formula:
$$\text{Atomic volume of individual atom}={\displaystyle \frac{4}{3}}\times \pi \times (r{)}^{3}p{m}^3$$

Note:
Both the methods of calculating atomic volume are correct. Atomic volume of a single atom can be calculated from the molar volume by dividing it with the Avogadro’s number, but it only gives an average estimate. The other method though more precise involves the use of high level technology.