Answer: [tex]0.51\times10^{-15}[/tex]
Step-by-step explanation:
We consider the shape of nucleus and the atom to be sphere.
Also , we know that the Volume of sphere = [tex]V=\dfrac{4\pi}{3}r^3[/tex]
Given : Radius of proton : [tex]r=1.0\times10^{-3}\text{ em}[/tex]
Since 1 em = 0.0042175176 metres
∴ [tex]r=1\times10^{-13}\times 0.0042175176\approx4.22\times10^{-16} \text{ m}[/tex]
Radius of atom : [tex]R=52.9 \text{ pm}[/tex]
Since, [tex]1\ \text{pm}=1\times10^{-12}[/tex]
∴Radius of atom : [tex]R=52.9\times10^{-12} =5.29\times10^{-11}\text{ m}[/tex]
Now, the fraction of the space within the atom is occupied by the nucleus :_
[tex]\dfrac{V(r)}{V(R)}=\dfrac{\dfrac{4\pi}{3}(4.22\times10^{-16} )^3}{\dfrac{4\pi}{3}(5.29\times10^{-11})^3}\\\\=(\dfrac{4.22}{5.29})^3\times\dfrac{10^{-48}}{10^{-33}}\\\\\approx0.51\times10^{-48+33}=0.51\times10^{-15}[/tex]
