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Question: Atomic radius is of the order of \({10^{ - 8}}cm\) and the nuclear radius is of the order of \({10^{...

Atomic radius is of the order of 10−8cm{10^{ - 8}}cm and the nuclear radius is of the order of 10−13cm{10^{ - 13}}cm. The fraction of atom occupied by nucleus is:
A. 10−5{10^{ - 5}}
B. 105{10^5}
C. 1015{10^{15}}
D. None of the above

Explanation

Solution

First find the volume of atom with given size and volume of nucleus of atom with given size. Then the fraction of atom occupied by nucleus is equal to fraction of volume of atom occupied by volume of nucleus of atom which is equal to ratio of the volume of nucleus to the volume of atom.

Complete step by step answer:
Atom consists of electrons, protons and neutrons. Protons and neutrons are present in small size nuclei present at the centre of an atom. And electrons are revolving around the nucleus in particular orbits. Size of the nucleus is too small in comparison to the size of an atom.
Given, atomic radius is of the order of 10−8cm{10^{ - 8}}cm and the nuclear radius is of the order of 10−13cm{10^{ - 13}}cm.
We know that the volume of the sphere is 43πr3\dfrac{4}{3}\pi {r^3}, where rr is the radius of the sphere.
Then the volume atom is given by
Vatom=43π(10−8)3=43π×10−24{V_{atom}} = \dfrac{4}{3}\pi {\left( {{{10}^{ - 8}}} \right)^3} = \dfrac{4}{3}\pi \times {10^{ - 24}}
And volume of nucleus is given by
Vnucleus=43π(10−13)3=43π×10−39{V_{nucleus}} = \dfrac{4}{3}\pi {\left( {{{10}^{ - 13}}} \right)^3} = \dfrac{4}{3}\pi \times {10^{ - 39}}
The fraction of an atom occupied by a nucleus is equal to the ratio of the volume of the nucleus to the volume of an atom. Then fraction of atom occupied by nucleus is given by
f=VnucleusVatom=43π×10−3943π×10−24f = \dfrac{{{V_{nucleus}}}}{{{V_{atom}}}} = \dfrac{{\dfrac{4}{3}\pi \times {{10}^{ - 39}}}}{{\dfrac{4}{3}\pi \times {{10}^{ - 24}}}}
f=10−3910−24=10−15f = \dfrac{{{{10}^{ - 39}}}}{{{{10}^{ - 24}}}} = {10^{ - 15}}
Then the fraction of atoms occupied by the nucleus is of the order of 10−15{10^{ - 15}}.

Hence correct answer is option C.

Note:
In an excited state, valence shell electrons move to higher orbit due to which size of atom may increase but the size of nucleus always remains same then the fraction of atom occupied by nucleus also changed. And the fraction of atoms occupied by the nucleus also vary from element to element.