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 × 10⁻¹⁵ A1/3 m. The approximate ratio of the nuclear density and water density is n × 10¹³. The value of n is __________. Numerical answer type. Work it out, then open the answer.

Answer: 11. ρN = (m)/(4/3π R₀³) = 1.6 × 10⁻²⁷4/3π (1.5 × 10⁻¹⁵)³ ρN = 1.6 × 10⁻²⁷1.414 × 10⁻⁴⁴ = 1.13 × 10¹⁷ kg/m³ (ρN)/(ρw) = 1.13 × 10¹⁷10³ = 11.3 × 10¹³ So n ≈ 11

Assume that protons and neutrons have equal masses. Mass of a nucleon… | JEE Main 2023 (24 Jan, Shift 1)

Q17JEE Main 2023 · 24 JAN · SHIFT 1Medium

Nucleus: Composition, Size & Nuclear Force

Assume that protons and neutrons have equal masses. Mass of a nucleon is $1.6 \times 10^{-27}$ kg and radius of nucleus is $1.5 \times 10^{-15}\,\text{A}^{1/3}$ m. The approximate ratio of the nuclear density and water density is $n \times 10^{13}$ . The value of $n$ is __________.

Numerical answer type. Work it out, then open the answer.

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Answer: 11

$\rho_N = \dfrac{m}{\frac{4}{3}\pi R_0^3} = \dfrac{1.6 \times 10^{-27}}{\frac{4}{3}\pi (1.5 \times 10^{-15})^3}$
$\rho_N = \dfrac{1.6 \times 10^{-27}}{1.414 \times 10^{-44}} = 1.13 \times 10^{17}\ \text{kg/m}^3$
$\dfrac{\rho_N}{\rho_w} = \dfrac{1.13 \times 10^{17}}{10^3} = 11.3 \times 10^{13}$
So $n \approx 11$

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