Question

The radius of the nucleus of an atom of mass number $216$ is $({{R}_{0}}=1.2\,fermi)$ :
$\begin{align}
  & A.\,\,7.2\times {{10}^{-15}}\,m \\
 & B.\,\,7.2\times {{10}^{-15}}\,fermi \\
 & C.\,\,14.4\times {{10}^{-15}}\,m \\
 & D.\,\,1.44\times {{10}^{-15}}\,mferm \\
\end{align}$

Answer 1

Hint: This is a simple question of finding the radius of the nucleus. We can do that using the formula, which is readily available and is widely used to find the radius of the nucleus. All the values related to the formula are given in the question, we need to just substitute the value in the formula and we will get the answer directly.

Formula used:
$R={{R}_{0}}.{{A}^{\dfrac{1}{3}}}$

Complete Step-by-Step solution :
We know that, radius of the nucleus can be calculated using the below formula,
$R={{R}_{0}}.{{A}^{\dfrac{1}{3}}}$
where, ${{R}_{0}}$ is a constant and the value for which is given in the question, and
$A$ is the mass number of an atom, which is also given in the question.
So, after substituting the value in the above equation, we get –
$\begin{align}
  & R=(1.2\,fermi).{{(216)}^{\dfrac{1}{3}}} \\
 & \Rightarrow R=(1.2\times {{10}^{-15}})(6)\,m \\
 & \therefore R=7.2\times {{10}^{-15}}\,m \\
\end{align}$
Hence, the radius of the nucleus of an atom is $7.2\times {{10}^{-15}}\,m$.

Therefore, the correct answer is Option (A).

Additional Information:
The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron in 1932, models for a nucleus composed of protons and neutrons were quickly developed by Dmitri Ivanenko and Werner Heisenberg. An atom is composed of a positively-charged nucleus, with a cloud of negatively-charged electrons surrounding it, bound together by electrostatic force. Almost all of the mass of an atom is located in the nucleus, with a very small contribution from the electron cloud. Protons and neutrons are bound together to form a nucleus by the nuclear force.

Note:
This is a simple question of substituting the value given in the question in the formula, just the one important thing that we should know is the formula for finding the radius of the nucleus of an atom. If the formula is known, then it becomes a simple question of finding the answer by substituting the value.