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 A^1/3 cm. The atomic radius of atom is 1 $\overset{o}{A}$ . If the mass no. is 64, the fraction of the atomic volume that is occupied by nucleus is

A
1.0 x 10^-3
B
5.0 x 10^-5
C
2.5 x 10^-2
D
1.25 x 10^-13

Solution:

$\frac{V_{n}}{V_{a}} = \frac{(4 / 3) {πr}_{n}^{3}}{(4 / 3) {πr}_{a}^{3}} = \frac{r_{n}^{3}}{r_{a}^{3}} = \frac{{[1 .25 \times 10^{- 13} \times (64)^{1 / 3}]}^{3}}{{(10^{- 8})}^{3}}$

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