JEE Main 2025 · 7 April · evening · Single correct · +4 / −1
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 ( 64₂₉ Cu) nucleus is greater than that of the carbon ( 12₆ 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) Both (A) and (R) are correct but (R) is not the correct explanation of (A)
- (c) (A) is not correct but (R) is correct
- (d) Both (A) and (R) are correct and (R) is the correct explanation of (A)
Answer and solution
Answer (c) (A) is not correct but (R) is correct
Solution
Physics sir · 4 steps
Write the density with R = R₀ A^(1/3) and watch the mass number cancel completely.
- Check the Reason. Experiments show a nucleus has radius R = R₀ A^(1/3), with R₀ ≈ 1.2 × 10⁻¹⁵ m. So (R) is correct.
- Build the density. The nuclear mass is about A m, where m is the mass of one nucleon. The volume is 4/3π R³ = 4/3π R₀³ A, so the volume also grows in step with A.
ρ = (A m)/(4/3π R₀³ A) = 3m/(4π R₀³)
- Compare the nuclei. A cancels, so the density does not depend on the mass number. ⁶⁴₂₉Cu and ¹²₆C have the same nuclear density, about 2.3 × 10¹⁷ kg m⁻³. So (A) is wrong.
- So. (A) is not correct but (R) is correct. In fact (R) is the very reason (A) fails. The answer is (c).
The idea to keep. Radius goes as A^(1/3), so volume goes as A, and so does mass. Every nucleus has roughly the same density, whether it is light or heavy.
Answer from the NTA final answer key. Solution by PrepWiser.