The unit of length convenient on the atomic s | vedclass

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Question

(A) Radius of hydrogen atom,$r = 0.5 \mathring{A} = 0.5 	imes 10^{-10} \, m$. Volume of one hydrogen atom $= \frac{4}{3} \pi r^{3} = \frac{4}{3} 	im

Vedclass · Accepted Answer

$3.16 	imes 10^{-7}$

Vedclass · Answer

(A) Radius of hydrogen atom,$r = 0.5 \mathring{A} = 0.5 	imes 10^{-10} \, m$. Volume of one hydrogen atom $= \frac{4}{3} \pi r^{3} = \frac{4}{3} 	imes 3.14159 	imes (0.5 	imes 10^{-10})^{3} \approx 0.5236 	imes 10^{-30} \, m^{3}$. $1$ mole of hydrogen contains $N_{A} = 6.022 	imes 10^{23}$ atoms. Total volume of $1$ mole of hydrogen atoms $= N_{A} 	imes 	ext{Volume of one atom} = 6.022 	imes 10^{23} 	imes 0.5236 	imes 10^{-30} \, m^{3} \approx 3.153 	imes 10^{-7} \, m^{3}$. Rounding to two decimal places,the result is $3.16 	imes 10^{-7} \, m^{3}$.

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

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