Question

The approximate radius of polonium nucleus of mass number 210 is:
(A) $8\times {{10}^{-6}}m$
(B) $8\times {{10}^{-5}}m$
(C) $4\times {{10}^{-6}}m$
(D) none of these

Answer 1

Hint: Recollect Rutherford's gold foil experiment. From Rutherford’s experiments, it was found that \[\text{Radius of any nucleus }=R={{R}_{0}}{{A}^{\dfrac{1}{3}}}\]

Complete answer:
Nucleus is the innermost core of an atom. We all are familiar with Rutherford’s experiment. From the experiment, Rutherford had made certain observations. One of the conclusions he made was that the radius of the nucleus is about ${{10}^{-15}}m$ or 1fm where fm is fermimeter.
We know the formula,
\[R={{R}_{0}}{{A}^{\dfrac{1}{3}}}\]
where R0 is a constant having the value $1.3\times {{10}^{-15}}m\,=1.3fm$
Polonium has an atomic mass number of 210.
So, A=210
Substituting the values, we get,
\[\begin{align}
  & R=1.3\times {{10}^{-15}}\times {{(210)}^{\dfrac{1}{3}}} \\
 & =7.727\times {{10}^{-15}}m \\
 & =7.727fm
\end{align}\]
Therefore, Radius of Polonium is 7.727fm which is approximately equal to 8fm.

Since, no values match the answer, option (D) is the correct option.

Additional Information:
We all have studied about the famous gold foil experiment which was performed by scientist Rutherford in 1909. It is also known as the $\alpha -\text{particle}$ scattering experiment. He placed a radioactive source of $\alpha -\text{particle}$ in the cavity of a lead block and $\alpha -\text{particles}$ were made to pass through lead slit to obtain a fine jet of $\alpha -\text{particles}$. This jet was bombarded on a thin gold foil having 100nm thickness. A fluorescent screen of ZnS surrounded the gold foil to capture any $\alpha -\text{particles}$ radiated from the foil.
He observed that most of the particles passed through the gold foil without any deflection. Some particles deflected through a small angle less than $90{}^\circ $, few particles deflected through a large angle greater than $90{}^\circ $ and very few particles deflected through an angle of $180{}^\circ $.
Rutherford concluded that an atom largely consists of an empty space. The positively charged $\alpha -\text{particles}$ get repelled by the positive charges present in the atom which results in deflection. He called this positively charged entity of the atom as ‘nucleus’. The volume occupied by the nucleus is negligible in comparison to the total volume of the atom. The radius of the atom is approximately ${{10}^{-10}}m$ (Angstrom unit) and the radius of the nucleus is approximately ${{10}^{-15}}m$ (Fermimeter).

Note:
Don’t get confused with the given values. Remember that the radius of the nucleus will always be equal to some fermometer.