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Assume that protons and neutrons have equal masses. Mass of a nucleon is 1.6×10⁻²⁷ kg and radius of nucleus is 1.5×10⁻¹⁵A^1/3 m. The approximate ratio of the nuclear density and water density is n×10¹³. The value of n is ______.

Asked in JEE Main 24th Jan 1st Shift 2023 · Nuclear radius and density

Answer: 11

Step-by-step solution

ρ=(3m)/(4π R₀³)=(3×1.6×10⁻²⁷)/(4π×3.375×10⁻⁴⁵)=1.13×10¹⁷ kg m⁻³

Ratio to water (10³): 1.13×10¹⁴=11.3×10¹³

→ 11

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