A nucleus has mass number A₁ and volume V₁. Another nucleus has mass number A₂ and Volume V₂. If relation between mass number is A₂=4 A₁, then V₂/V₁= __________.

Solution

Physics sir · 3 steps

Nuclear volume grows in step with mass number, so four times the nucleons means four times the volume.

1. Size of a nucleus. The radius of a nucleus follows R = R₀ A^(1/3), where R₀ ≈ 1.2 fm is the same for every nucleus.

   V = 4/3π R³ = 4/3π R₀³ A ⇒ V ∝ A

2. Take the ratio. Cubing A^(1/3) gives back A, so V₂/V₁ = A₂/A₁ = 4A₁/A₁.
3. So. V₂/V₁ = 4.

The common slip: 1.59. Treating the radius ratio as the answer gives 4^(1/3) ≈ 1.59, not 4. The question asks for volume, so cube the radius ratio.

The idea to keep. Since R ∝ A^(1/3), nuclear volume goes as A. That is why every nucleus has nearly the same density: mass and volume both scale with A.

Answer from the NTA final answer key. Solution by PrepWiser.