Atoms & Nuclei

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Question 174 of 239

The radius RR of a nucleus of mass number AA can be estimated by the formula R=(1.3×10−15)A1/3mR=\left(1.3\times {10}^{-15}\right){A}^{1/3}m. It follows that the mass density of n nucleus is of the order of: (Mprot≅Mneut≃1.67×10−27kg)\left({M}_{prot}\cong {M}_{\text{neut}}≃1.67\times {10}^{-27}kg\right)

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Answer: (D) 1017kgm−3{10}^{17}kg{m}^{-3}

ρnucleus = mass  volume \rho_{\text {nucleus }}=\frac{\text { mass }}{\text { volume }}
=A(4/3)πr03 A=34πr03=\frac{A}{(4 / 3) \pi r_0^3 \mathrm{~A}}=\frac{3}{4 \pi \mathrm{r}_0^3}
=2.3×1017 kg/m3=2.3 \times 10^{17} \mathrm{~kg} / \mathrm{m}^3

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