JEE Mains 2025 Nuclear Mass Density Question | 8 April Shift 2 PYQ with Solution
This post covers a JEE Mains 2025 Physics question from the 8th April Shift 2 paper. The question tests your understanding of nuclear mass density — a key concept in Modern Physics. Let’s break it down with a clear step-by-step explanation and a full video solution.
Question
For a nucleus of mass number A and radius R, the mass density of nucleus can be represented as:
- (1) A³
- (2) A²⁄³
- (3) 1⁄A³
- (4) Independent of A
Note: This question appeared in the JEE Mains 2025 Physics 8th April Shift 2 paper.
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Detailed Step-by-Step Solution
Step 1: Recall the formula for nuclear radius
The radius of a nucleus is given by the empirical formula: R = R₀ × A1/3, where R₀ is a constant and A is the mass number.
Step 2: Volume of the nucleus
We consider the nucleus to be spherical, so the volume is:
V = (4/3)πR³ = (4/3)π(R₀³ × A).
Step 3: Mass of the nucleus
The mass of the nucleus is approximately proportional to A (since mass number ≈ total nucleons): M ∝ A.
Step 4: Define mass density
Density is mass divided by volume:
ρ = M / V = A / [(4/3)πR₀³ × A] = constant
Step 5: Final answer
As A cancels out, we conclude that the mass density of the nucleus is independent of A.
✅ Correct Option: (4) Independent of A
Watch the Full Video Solution
Watch this complete video explanation on our YouTube channel:
Conclusion
This question reinforces the idea that nuclear mass density is a constant, independent of the mass number A. This concept is frequently tested in Modern Physics sections of competitive exams like JEE.
