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If an atom were enlarged to the size of the earth ( $ R = {10^7}m $ ), how large would its nucleus be?
(A) $ {10^4}m $
(B) $ {10^3}m $
(C) $ {10^2}m $
(D) $ {10^5}m $

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Last updated date: 13th Jun 2024
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Answer
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Hint: Atoms are composed of electrons that surround a central nucleus. The radius of an atom is around 1 to 2. 5 angstroms ( $ \mathop {\text{A}}\limits^{\text{o}} $ ), where the radius of a nucleus is about $ {\text{1}}{{\text{0}}^{{\text{ - 5}}}}\mathop {\text{A}}\limits^{\text{o}} $ .We can compare the sizes of the nucleus to that of a typical atom to get the answer.

Complete step by step solution:
Atoms are defined as the basic building blocks of matter. It is the smallest constituent unit of matter that possesses the properties of the chemical element. Atoms don’t exist independently, instead, they form ions and molecules which further combine in large numbers to form matter that we see, feel and touch.
The size of an atom is extremely small, much smaller than our imagination. A layer of an atom as thick as a thin sheet of paper is formed when more than millions of atoms are stacked together. It is impossible to measure the size of an isolated atom because it’s difficult to locate the positions of electrons surrounding the nucleus.
However, the size of an atom can be estimated by assuming that the distance between adjacent atoms is equal to half the radius of an atom. Atomic radius is generally measured in nanometers.
The radius of a typical atom is around 1 to 2. 5 angstroms ( $ \mathop {\text{A}}\limits^{\text{o}} $ ), where the radius of a nucleus is about $ {\text{1}}{{\text{0}}^{{\text{ - 5}}}}\mathop {\text{A}}\limits^{\text{o}} $ .
It has been given that an atom is enlarged to the size of the earth of radius $ R = {10^7}m $ .
Hence, we can say that, if an atom were enlarged to the size of the earth, its nucleus would be only $ {10^2}m $ in diameter and could easily fit inside a small football stadium.
Thus, the correct answer is Option C.

Note:
Atoms consist of three fundamental types of particles, protons, electrons and neutrons. Neutrons and protons have approximately the same mass and in contrast to this the mass of an electron is negligible. A proton carries a positive charge, a neutron has no charge and an electron is negatively charged. An atom contains equal numbers of protons and electrons and therefore overall an atom has no charge. The nucleus of an atom contains protons and neutrons only, and therefore is positively charged. The electrons occupy the region of space around the nucleus. Therefore, most of the mass is concentrated within the nucleus.