Assertion (A): The density of a copper-64 nucleus is greater than the density of a carbon-12 nucleus. Reason (R): Nuclear radius is proportional to $\left(A^{\frac13}\right)$ where A is the mass number. Choose the correct answer.
Options

Question

Assertion (A): The density of a copper-64 nucleus is greater than the density of a carbon-12 nucleus. Reason (R): Nuclear radius is proportional to $\left(A^{\frac13}\right)$ where A is the mass number. Choose the correct answer.

Options

G1 Physics · Accepted Answer

Nuclear mass is approximately proportional to mass number A: M ∝ A. Nuclear radius is R = R₀ A ( 1 / 3 ) , A^(1/3), A ( 1/3 ) , so nuclear volume is V ∝ R³ ∝ A. Therefore nuclear density is ρ = M/V ∝ A/A, which is approximately constant for all nuclei. Thus the copper nucleus is not denser simply because A is larger. Assertion A is false. The radius relation R∝ A ( 1 / 3 ) A^(1/3) A ( 1/3 ) is true. Correct option: B.

Assertion (A): The density of a copper-64 nucleus is greater than the density of a carbon-12 nucleus. Reason (R): Nuclear radius is proportional to ( A 1 3 ) \left(A^{\frac13}\right) ( A 3 1 ​ ) where A is the mass number. Choose the correct answer.

Assertion (A): The density of a copper-64 nucleus is greater than the density of a carbon-12 nucleus. Reason (R): Nuclear radius is proportional to ( A 1 3 ) \left(A^{\frac13}\right) ( A 3 1 ) where A is the mass number. Choose the correct answer.