Answer to Question #28808 in Physics for Abhishek

Question

The size of a hydrogen atom is about 0.5 Angstrom. What is total atomic volume in m3 of a mole of hydrogen atom?

Answer 1

A mole of anything contains an Avogadro constant of constituent particles, which is about 6.022 * 10^23 particles/mole.
Thus, in one mole of atomic Hydrogen (H) there is this many H atoms. If diameter of each is about d = 0.5 A, the volume of one molecule is (assuming spherical shape)
V = (4/3)*pi*(d/2)^3 = (4/3)*pi*(0.5 * 10^(-10) m / 2)^3 = 6.545 * 10^(-32) m^3.
To get the atomic volume of a mole of H atoms, we'll multiply this elementary volume by the number of atoms in a mole:
V_a = 6.545 * 10^(-32) (m^3 / atom) * 6.022 * 10^23 (atoms / mole) = 3.94 * 10^(-8) m^3.