Question

The radius of a nucleus is directly proportional to:
$\begin{align}
& a){{A}^{2}} \\
& b){{A}^{1/3}} \\
& c){{A}^{3}} \\
& d)A \\
\end{align}$

Answer 1

Hint: The nucleus can be thought of as a sphere and it is known that volume of a nucleus is proportional to its mass number. The density of a nucleus is independent of its atomic and mass number.

Complete step by step answer:
> Rutherford was the first one to discover the existence of a positively charged centre inside an atom, which was later named as nucleus. The size of a nucleus is much smaller than that of an atom. It can be comparable to a tennis ball (the nucleus) kept at the centre of a football field (the atom).
> In the famous gold-foil experiment, Rutherford discovered that most of the space inside an atom is empty and all of the mass is concentrated at its centre. But he made one mistake; he assumed that the bending of the alpha particles when they hit the thin gold-foil is only because of the coulombic repulsion forces because of the like nature of charges. As was seen later, this was not the case. Experiments continued and it was noticed that when higher energy alpha particles were bombarded at the thin gold-foil, a new force caused the repulsion which was way stronger than the forces of coulomb. These were later termed as the nuclear force which operated at a very short range but was stronger than any other force.
> This force was responsible for holding together the nucleons. The nucleons are the species that occupy a nucleus of an atom belonging to any species. The size of the nucleus was found out by bombarding high energy electrons in place of alpha particles. The following formula was derived for this purpose:
                                                        \[R={{R}_{o}}{{A}^{1/3}}\]

Where “R” is the radius of the nucleus, “${{R}_{o}}$” is the constant which has value equal to $1.2\times {{10}^{-15}}m $and “A” is the mass number of the atom.

The answer to the above question is option (b).

Note: The above equation for the radius of a nucleus is valid for atoms of all elements. The mass number “A” is the sum of the total number of protons and neutrons present inside a nucleus. The density of a nucleus is independent of its mass number. It means the density of a nucleus belonging to an atom of any element is the same