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  4. The radius of R of a nucleus of mass number A can be estimated by the formula R =(1.3 × 10-15) A 1 / 3 m It follows that the mass density of a nucleus is of the order of: ( M text prot. ≅ M text neut. ≃ 1.67 × 10-27 kg )

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Q. The radius of $R$ of a nucleus of mass number A can be estimated by the formula $R =\left(1.3 \times 10^{-15}\right) A ^{1 / 3} m$ It follows that the mass density of a nucleus is of the order of:
$\left( M _{\text {prot. }} \cong M _{\text {neut. }} \simeq 1.67 \times 10^{-27} kg \right)$

JEE MainJEE Main 2020Nuclei

Solution:

$\rho_{\text {nucleus }} =\frac{\text { mass }}{\text { volume }}=\frac{ A }{(4 / 3) \pi r _{0}^{3} A } $
$=\frac{3}{4 \pi t _{0}^{3}}=2.3 \times 10^{17} \,kg / m ^{3} $