The ratio of atomic volume of nuclear volume is of the order of (A) \(10^{-15}\) (B) \(10^{-10}\) (C) \(10^{15}\) (D) \(10^{-10}\)

To find the atomic volume, remember that the majority of the volume of an atom is mostly empty space, with the electrons orbiting the nucleus at a distance. The radius of an atom (called the atomic radius) is typically around 1 Ångström (1 Å = \(10^{-10}\) meters). The volume of a sphere can be calculated using the formula: \[V = \frac{4}{3}\pi r_{a}^3\] Here, the atomic radius is denoted by \(r_{a}\) and is approximately \(10^{-10}\) meters.

To find the nuclear volume, understand that the nucleus is much smaller than the atom itself. The nuclear radius (denoted by \(r_{n}\)) is approximately \(10^{-15}\) meters. Again, we can use the formula for the volume of a sphere: \[V = \frac{4}{3}\pi r_{n}^3\]

Now we'll calculate the ratio of the atomic volume to the nuclear volume. \[\frac{V_{a}}{V_{n}} = \frac{\frac{4}{3}\pi r_{a}^3}{\frac{4}{3}\pi r_{n}^3}\] Since both atomic and nuclear volumes are spheres, we can simplify the equation by cancelling out the \(\frac{4}{3}\pi\) terms: \[\frac{V_{a}}{V_{n}} = \frac{r_{a}^3}{r_{n}^3}\] Now, substitute the values of the atomic and nuclear radii: \[\frac{V_{a}}{V_{n}} = \frac{(10^{-10})^3}{(10^{-15})^3}\] This ratio simplifies to: \[\frac{V_{a}}{V_{n}} = \frac{10^{-30}}{10^{-45}}\] After dividing the exponential terms, we are left with: \[\frac{V_{a}}{V_{n}} = 10^{15}\] So, the ratio of the atomic volume to the nuclear volume is of the order of \(10^{15}\), which corresponds to option (C).