The unit of length convenient on the atomic scale is known as an angstrom ($1 ext{ \AA} = 10^{-10}\

Question

The unit of length convenient on the atomic scale is known as an angstrom ($1	ext{ \AA} = 10^{-10}	ext{ m}$). The radius of a hydrogen atom is about $0.5	ext{ \AA}$. What is the total atomic volume in $	ext{m}^3$ of a mole of hydrogen atoms?

Professor PC Thomas Classes · Answer

Volume of 1 H-atom $= \frac{4}{3}\pi r^3 = \frac{4}{3} 	imes 3.14 	imes (0.5 	imes 10^{-10})^3 \approx 5.236 	imes 10^{-31}	ext{ m}^3$. Total volume for 1 mole $= V 	imes N_A = 5.236 	imes 10^{-31} 	imes 6.02 	imes 10^{23} \approx 3.15 	imes 10^{-7}	ext{ m}^3 \approx 3 	imes 10^{-7}	ext{ m}^3$.