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 × \(10^{-7}\text m^3\)