Assertion (A): The density of the copper nucleus is greater than that of the carbon nucleus. Reason (R): The nucleus of mass number A has a radius proportional to . [2025]

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Solution

Q.
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). [2025]

Assertion (A): The density of the copper $({}_{29}^{64}C u)$ nucleus is greater than that of the carbon $({}_{6}^{12}C)$ nucleus.

Reason (R): The nucleus of mass number A has a radius proportional to $A^{1 / 3}$ .

In the light of the above statements, choose the most appropriate answer from the options given below:

1 (A) is correct but (R) is not correct

2 (A) is not correct but (R) is correct

3 Both (A) and (R) are correct and (R) is the correct explanation of (A)

4 Both (A) and (R) are correct but (R) is not the correct explanation of (A)

Ans.
(2)

$ρ = \frac{M}{V} = \frac{m_{n} \times A}{\frac{4}{3} π R^{3}} = \frac{m_{n} \times A}{\frac{4}{3} π A R_{0}^{3}}$

So $ρ$ is almost constant, density of nucleus is independent of mass number.

$R = R_{0} A^{1 / 3} \Rightarrow R \propto A^{1 / 3}$

Radius is proportional to $A^{1 / 3}$ .

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