The density (in {kg}\,{m}^{-3} ) of nuclear matter is of the order of [AP EAPCET 23 May 2025 S2]

Correct Answer is : 101710¹7}1017

Correct Answer is : 101710¹7}1017

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Atoms and Nuclei

Section: Physics

Question : 4 of 33

Marks: +1, -0

The density (in

\mathrm{kg}\,\mathrm{m}^{-3}

Solution:

A nucleus has:

Radius

R=R_0 A^{\frac{1}{3}}

where

R_0 \approx 1.2 \times 10^{-15} \,\mathrm{m}

Each nucleon (proton or neutron) has a mass

m_n \approx 1.67 \times 10^{-27} \,\mathrm{kg}

Step 2: Estimate the number of nucleons per unit volume

For nuclear matter, the volume per nucleon is roughly the volume of a sphere of radius

R_0

V_{\;\text{per nucleon}\;} \;\; \approx \;\frac{4}{3} \pi R_0^3

V_{\;\text{per nucleon}\;} \;\; \approx \;\frac{4}{3} \pi (1.2 \times 10^{-15})^3 \approx 7.2 \times 10^{-45} \,\mathrm{m}^3

Hence, number density of nucleons:

n=\;\frac{1}{V_{\;\text{per nucleon}\;}} \approx \;\frac{1}{7.2 \times 10^{-45}} \approx 1.4 \times 10^{44} \,\mathrm{m}^{-3}

Step 3: Compute the mass density

\rho = n \times m_n = (1.4 \times 10^{44}) (1.67 \times 10^{-27}) \approx 2.3 \times 10^{17} \,\mathrm{kg}\,\mathrm{m}^{-3}

Density of nuclear matter

\sim 10^{17} \,\mathrm{kg}\,\mathrm{m}^{-3}

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