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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 ( 29^64 Cu ) 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 :

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

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

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

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

Atoms & Nuclei

JEE Main level, single correct, medium

162 of 239

Question 162 of 239

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 $\left({ }_{29}^{64} \mathrm{Cu}\right)$ nucleus is greater than that of the carbon $\left({ }_6^{12} \mathrm{C}\right)$ nucleus.
Reason (R): The nucleus of mass number A has a radius proportional to $\mathrm{A}^{1 / 3}$ .
In the light of the above statements, choose the most appropriate answer from the options given below :

Show answer and solution

Answer: (B) $(\mathrm{A})$ is not correct but $(\mathrm{R})$ is correct

\rho=\frac{\mathrm{M}}{\mathrm{~V}}=\frac{\mathrm{m}_{\mathrm{n}} \times \mathrm{A}}{\frac{4}{3} \pi \mathrm{R}^3}=\frac{\mathrm{m}_{\mathrm{n}} \times \mathrm{A}}{\frac{4}{3} \pi \mathrm{AR}_0^3}

\rho

is almost is constant
$\begin{aligned}
& \mathrm{R}=\mathrm{R}_0 \mathrm{~A}^{1 / 3} \\
& \mathrm{R} \propto \mathrm{~A}^{1 / 3}
\end{aligned}$

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