Question

The radius of atom is of the order of 1 Å and radius of nucleus if of the order of Fermi. How many magnitudes higher is the volume of atom as compared to the volume of nucleus?

Answer 1

Given: 

Radius of atom, r_a = 1 Å = 10^-10 m

Radius of nucleus, r_n = 1 fermi = 10^-15 m

Volume of atom; \(V_1 = \frac{4}{3}\pi r^3_a\)

Volume of nucleus,\(V_2 = \frac{4}{3}\pi r^3_n\)

\(\frac{V_1}{V_2}\,=\,\frac{\frac{4}{3}\pi r^3}{\frac{4}{3}\pi r_n^3}\,=\,(\frac{r_a}{r_n})^3\,=\,(\frac{10^{-10}}{10^{-15}})^3\,=10^{15}\)