Question
Four statements are given ( $A$ is mass number):
A. The volume of a nucleus is proportional to $A^{1/3}$.
B. The volume of a nucleus is proportional to $A$.
C. The difference in mass of an atom and its nucleus is called the mass defect.
D. The difference in mass of a nucleus and its constituents is called the mass defect.
Choose the correct answer from the options given below:
Options
Solution
Sol. [Key Concept: Nuclear mass number & related statements] As we know,
$$\begin{matrix} & \text{~}\text{Size of nucleus,}\text{~}r = r_{0}(A)^{\frac{1}{3}} \\ & \ \Rightarrow \ r^{3} = r_{0}^{3} \cdot A \\ & \ \Rightarrow \ V \propto A\ \left( \because V = \frac{4}{3}\pi r^{3} \right) \end{matrix}$$
So, option A → wrong and B → correct
while the difference between the actual mass of nucleus and its constituents is called the mass defect.
$$\therefore\ \text{~}\text{option}\text{~}C \rightarrow \text{~}\text{wrong and}\text{~}D \rightarrow \text{~}\text{correct}\text{~}$$
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