Question

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). 
Assertion (A): The density of the copper ($^{64}Cu$) nucleus is greater than that of the carbon ($^{12}C$) 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:

• A. (A) is correct but (R) is not correct
• B. (A) is not correct but (R) is correct
• C. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• D. Both (A) and (R) are correct but (R) is not the correct explanation of (A)

Hint:

Nuclear density remains approximately constant for all nuclei. The formula \( R \propto A^{1/3} \) describes the relationship between the radius and the mass number, but does not affect the overall density of the nucleus.

Answer 1

The Correct Option is B

To evaluate the Assertion (A) and Reason (R), we will analyze each statement and their relationship.

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

This assertion concerns the comparative densities of copper and carbon nuclei. Nuclear density is generally constant across all nuclei, irrespective of their size or element. This constancy arises because nuclear volume scales with the number of nucleons ($A$), as the radius ($r$) is proportional to $A^{1/3}$. Consequently, density ($\rho = \text{mass}/\text{volume}$) is approximately uniform. Therefore, the assertion that the density of a copper nucleus exceeds that of a carbon nucleus is false.

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

This statement is a fundamental principle in nuclear physics. The radius ($R$) of a nucleus is expressed as:

R = R_0 \cdot A^{1/3}

where $R_0$ is a constant. This formula indicates that nuclear radius increases with the cube root of the mass number. Thus, the reason provided is accurate.

In summary:

• Assertion (A) is incorrect because nuclear density is remarkably consistent across different elements and nuclei.
• Reason (R) is correct as it accurately describes the proportionality between nuclear radius and mass number.

The correct conclusion is:

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