Answer:
(a). The volume of the atom is ![6.23\times10^{-31}\ m^3](https://tex.z-dn.net/?f=6.23%5Ctimes10%5E%7B-31%7D%5C%20m%5E3)
(b). The volume of the nucleus is ![4.18\times10^{-45}\ m^3](https://tex.z-dn.net/?f=4.18%5Ctimes10%5E%7B-45%7D%5C%20m%5E3)
(c). The percentage of the volume of the atom that is occupied by the nucleus is ![6.70\times10^{-13}](https://tex.z-dn.net/?f=6.70%5Ctimes10%5E%7B-13%7D)
Explanation:
Given that,
Radius of nucleus ![r_{n}=1\times10^{-15}\ m](https://tex.z-dn.net/?f=r_%7Bn%7D%3D1%5Ctimes10%5E%7B-15%7D%5C%20m)
Radius of atom ![r=5.3\times10^{-11}\ m](https://tex.z-dn.net/?f=r%3D5.3%5Ctimes10%5E%7B-11%7D%5C%20m)
(a). We need to calculate the volume of the atom
Using formula of volume of the atom
![V=\dfrac{4\pi\times r^3}{3}](https://tex.z-dn.net/?f=V%3D%5Cdfrac%7B4%5Cpi%5Ctimes%20r%5E3%7D%7B3%7D)
Where, r = radius of atom
Put the value into the formula
![V=\dfrac{4\pi\times(5.3\times10^{-11})^3}{3}](https://tex.z-dn.net/?f=V%3D%5Cdfrac%7B4%5Cpi%5Ctimes%285.3%5Ctimes10%5E%7B-11%7D%29%5E3%7D%7B3%7D)
![V=6.23\times10^{-31}\ m^3](https://tex.z-dn.net/?f=V%3D6.23%5Ctimes10%5E%7B-31%7D%5C%20m%5E3)
(b). We need to calculate the volume of the nucleus
Using formula of volume of the nucleus
![V'=\dfrac{4\pi\times r^3}{3}](https://tex.z-dn.net/?f=V%27%3D%5Cdfrac%7B4%5Cpi%5Ctimes%20r%5E3%7D%7B3%7D)
Where, r = radius of atom
Put the value into the formula
![V'=\dfrac{4\pi\times(1\times10^{-15})^3}{3}](https://tex.z-dn.net/?f=V%27%3D%5Cdfrac%7B4%5Cpi%5Ctimes%281%5Ctimes10%5E%7B-15%7D%29%5E3%7D%7B3%7D)
![V'=4.18\times10^{-45}\ m^3](https://tex.z-dn.net/?f=V%27%3D4.18%5Ctimes10%5E%7B-45%7D%5C%20m%5E3)
(c). We need to calculate the percentage of the volume of the atom that is occupied by the nucleus
![percentage=\dfrac{V'}{V}\times100](https://tex.z-dn.net/?f=percentage%3D%5Cdfrac%7BV%27%7D%7BV%7D%5Ctimes100)
Put the value into the formula
![percentage=\dfrac{4.18\times10^{-45}}{6.23\times10^{-31}}\times100](https://tex.z-dn.net/?f=percentage%3D%5Cdfrac%7B4.18%5Ctimes10%5E%7B-45%7D%7D%7B6.23%5Ctimes10%5E%7B-31%7D%7D%5Ctimes100)
![percentage=6.70\times10^{-13}](https://tex.z-dn.net/?f=percentage%3D6.70%5Ctimes10%5E%7B-13%7D)
Hence, (a). The volume of the atom is ![6.23\times10^{-31}\ m^3](https://tex.z-dn.net/?f=6.23%5Ctimes10%5E%7B-31%7D%5C%20m%5E3)
(b). The volume of the nucleus is ![4.18\times10^{-45}\ m^3](https://tex.z-dn.net/?f=4.18%5Ctimes10%5E%7B-45%7D%5C%20m%5E3)
(c). The percentage of the volume of the atom that is occupied by the nucleus is ![6.70\times10^{-13}](https://tex.z-dn.net/?f=6.70%5Ctimes10%5E%7B-13%7D)