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Q.
The ratio of the volume of the atom to the volume of the nucleus is of the order of
Physical World, Units and Measurements
Solution:
Radius of the atom, $R_{a}=1\,\mathring{A} =10^{-10}\,m$
Volume of the atom, $V_{a}=\frac{4}{3} \pi R^{3}_{a}=\frac{4}{3}\times\pi\times\left(10^{-10}\right)^{3}\,m^{3}$
Radius of the nucleus, $R_n=1$ fermi $=10^{-15}\,m$
Volume of the nucleus, $V_{n}=\frac{4}{3} \pi R^{3}_{n}=\frac{4}{3}\times\pi\times\left(10^{-15}\right)^3\,m^{3}$
Their corresponding ratio is
$\frac{V_{a}}{V_{n}}=\frac{\left(10^{-10}\right)^{3}}{\left(10^{-15}\right)^{3}}=\frac{10^{-30}}{10^{-45}}=10^{15}$