The nucleus and an atom can be assumed to be spherical. The radius of the nucleus of mass no. A is given by 1.25 x 10-13 x A1/3 cm. The atomic radius of atom is 1 Ao . If the mass no. is 64, the fraction of the atomic volume that is occupied by nucleus is

# The nucleus and an atom can be assumed to be spherical. The radius of the nucleus of mass no. A is given by 1.25 x 10-13 x A1/3 cm. The atomic radius of atom is 1 $\stackrel{\mathrm{o}}{\mathrm{A}}$ . If the mass no. is 64, the fraction of the atomic volume that is occupied by nucleus is

1. A

1.0 x 10-3

2. B

5.0 x 10-5

3. C

2.5 x 10-2

4. D

1.25 x 10-13

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### Solution:

$\frac{{\mathrm{V}}_{\mathrm{n}}}{{\mathrm{V}}_{\mathrm{a}}}=\frac{\left(4/3\right){\mathrm{\pi r}}_{\mathrm{n}}^{3}}{\left(4/3\right){\mathrm{\pi r}}_{\mathrm{a}}^{3}}=\frac{{\mathrm{r}}_{\mathrm{n}}^{3}}{{\mathrm{r}}_{\mathrm{a}}^{3}}=\frac{{\left[1.25×{10}^{-13}×\left(64{\right)}^{1/3}\right]}^{3}}{{\left({10}^{-8}\right)}^{3}}$

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