Question

The unit of length convenient on the atomic scale is known as an angstrom and is denoted by $\AA$ : 1 $\AA$ = $10^{-10}\;\text m$. The size of a hydrogen atom is about 0.5$\AA .$ What is the total atomic volume in m3 of a mole of hydrogen atoms ?

Answer 1

Radius of hydrogen atom, r = 0.5 $\AA$ = 0.5 × $10^{-10}\;\text m$
Volume of hydrogen atom = $\frac{4}{3}\pi r ^3$
=$\frac{4}{3}\times\frac{22}{7}\times(0.5 \times10^{-10})^3$
= 0.524 × $10^{-30} \text m^3$
1 mole of hydrogen contains $6.023$× $10^{23}$ hydrogen atoms.
$\therefore$ Volume of 1 mole of hydrogen atoms =$6.023$ × $10^{23}$× $0.524$ × $10^{-30}$
= 3.16 × $10^{-7}\text m^3$