The radius R of a nucleus of mass number A can be estimated by the formula R = 1 . 3 × 10 - 15 A 1 / 3…

The radius R of a nucleus of mass number A can be estimated by the formula R=1.3×10-15A1/3m. It follows that the mass density of n nucleus is of the order of: Mprot≅Mneut ≃1.67×10-27 kg
  1. 103 kg m-3
  2. 1010 kg m-3
  3. 1024 kg m-3
  4. 1017 kg m-3

Solution

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

Asked in: JEE Main 2020 (03 Sep Shift 2)

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