Question

The unit of length convenient on the atomic scale is known as an angstrom and is denoted by $\mathring{A}.1\mathring{A}=10^{-10}m$. The size of the hydrogen atom is about $0.5\mathring{A}$ The total atomic volume in $m^3$ of a mole of hydrogen atoms would be

• A. $3.15\times 10^{-7}{m}^3$
• B. $3.0\times 10^{-8}{m}^3$
• C. $3.85\times 10^{-7}{m}^3$
• D. $2.85\times 10^{-7}{m}^3$

Answer 1

Answer: (A)

Radius of hydrogen atom $(r)=0.5\mathring{A}=0.5\times 10^{-10}m$
Volume of each hydrogen atom $(V)=\frac{4}{3}\pi r^3$
$=\frac{4}{3}\times 3.14\times {\left(0.5\times 10^{-10}\right)}^3$
$=5.234\times 10^{-31}{m}^3$
Number of atoms in one mole of hydrogen
$=$ Avogadro number $(N)$
$=6.023\times 10^{23}$
$\therefore$ Atomic volume of 1 mole of hydrogen atoms $(V^{\prime })$
$=$ Volume of a hydrogen atom $\times$ Number of atoms
$V^{\prime }=V\times N$
$=5.236\times 10^{-31}\times 6.023\times 10^{23}{m}^3$
$=3.152\times 10^{-7}{m}^3$