Question

The radius of a hydrogen atom is $0.5\mathring{A}$. Find the order of magnitude of volume of $1$ mole hydrogen in $m^3$. Given that 1 mole of hydrogen has $6.02\times {10}^{23}$ hydrogen atoms.

• A. $2\times {10}^{-4}{m}^3$
• B. ${10}^{-3}{m}^3$
• C. ${10}^{-7}{m}^3$
• D. ${10}^{-2}{m}^3$

Answer 1

The correct option is C ${10}^{-7}{m}^3$

Volume of 1 hydrogen atom, $V=4\pi r^3/3;r=0.5\times {10}^{-10}m$

So, $V=0.5245\times {10}^{-30}{m}^3$

So, volume of 1 mole ($6.02\times {10}^{23}$) is $V\times 6.02\times {10}^{23}=3.157\times {10}^{-7}{m}^3$

So, order of magnitude is ${10}^{-7}{m}^3$.