Answer
The proton occupies $\frac{1}{1.48 \times 10^{14}}$ of the volume of the atom , or $6.755 \times 10^{-15} $ percent.
Work Step by Step
1. Calculate the volume of the atom by using conversion $1pm= 10^{-19}cm$ and $52.9 pm = 5.29 \times 10 ^{-9} cm$.
$V_{at}= \frac{4 \times π \times r^{3}}{3}= \frac{4 \times 3.14 \times (5.29 \times 10^{-9}cm)^{3}}{3} = 6.2009 \times 10^{-25} cm^{3} $
2. Calculate the volume of the proton:
$V_{p} = \frac{4 \times π \times r^{3}}{3}= \frac{4 \times 3.14 \times (1.0 \times 10^{-13}cm)^{3}}{3} = 4.1888 \times 10^{-39} cm^{3} $
3. To find ration, divide the volume of proton by the volume of the atom:
$\frac{V_{p}}{V_{at}} = \frac{4.1888 \times 10^{-39} cm^{3}}{6.2009 \times 10^{-25} cm^{3}}=\frac{1}{1.48 \times 10^{14}}=6.755 \times 10^{-15} $
