Nuclei · Class 12 · CBSE · Science Physics

What is the nuclear density of a nucleus having mass number A, given that R0 = 1.2 times 10^{-15}text{ m} and the average mass of a nucleon is 1.67 t…

Practice question from Nuclei (Class 12 · CBSE · Science Physics), with the correct answer and a step-by-step solution.

medium · MCQ · Q-1BA2BA

What is the nuclear density of a nucleus having mass number AA, given that R0=1.2×10−15 mR_0 = 1.2 \times 10^{-15}\text{ m} and the average mass of a nucleon is 1.67×10−27 kg1.67 \times 10^{-27}\text{ kg}?

  1. A.2.3×1017 kg m−32.3 \times 10^{17}\text{ kg m}^{-3}Correct answer
  2. B.1.16×1015 kg m−31.16 \times 10^{15}\text{ kg m}^{-3}
  3. C.2.3×1014 kg m−32.3 \times 10^{14}\text{ kg m}^{-3}
  4. D.4.6×1017 kg m−34.6 \times 10^{17}\text{ kg m}^{-3}

Solution

Nuclear density ρ=MassVolume=Am(4/3)πR03A=3m4πR03\rho = \frac{\text{Mass}}{\text{Volume}} = \frac{A m}{(4/3)\pi R_0^3 A} = \frac{3m}{4\pi R_0^3}. Substituting the values, ρ=3×1.67×10−274×3.14×(1.2×10−15)3≈2.3×1017 kg m−3\rho = \frac{3 \times 1.67 \times 10^{-27}}{4 \times 3.14 \times (1.2 \times 10^{-15})^3} \approx 2.3 \times 10^{17}\text{ kg m}^{-3}. Notice that density is independent of mass number AA.

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