Question 137: Atoms & Nuclei

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 $(^ {64}_{29} 	ext{Cu})$ nucleus is greater than that of the carbon $(^ {12}_{6} 	ext{C})$ 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 :

Accepted Answer

To evaluate the assertion and reason provided, we need to consider the formula for the density of a nucleus. The density $ ho $ can be expressed as follows:
$ ho = \frac{M}{V} = \frac{m_n 	imes A}{\frac{4}{3} \pi R^3} $
Here, $ m_n $ represents the nucleon mass, $ A $ is the mass number, and $ R $ is the radius of the nucleus. According to the formula for the radius:
$ R = R_0 A^{1/3} $
This indicates that the radius $ R $ is proportional to $ A^{1/3} $. By substituting the expression for $ R $ in terms of $ A $ back into the formula for density, we get:
$ ho = \frac{m_n 	imes A}{\frac{4}{3} \pi (A^{1/3} R_0)^3} $
Simplifying the equation shows that the $ A $ terms cancel out:
$ ho = \frac{m_n}{\frac{4}{3} \pi R_0^3} $
This reveals that the nuclear density $ ho $ is approximately constant and independent of the mass number $ A $. Therefore, the densities of copper $(^{64}_{29} 	ext{Cu})$ and carbon $(^{12}_{6} 	ext{C})$ nuclei are effectively the same because the density formula results in a similar value regardless of the specific mass number.

Answer

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

Answer

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

Answer

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

Answer

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

Atoms & Nuclei

Choose the correct answer: