Roughly what percentage of an atom's volume is occupied by its nucleus?

• A. Nearly 100%
• B. About 1%
• C. Less than 0.01%
• D. Approximately 10%

Answer: (C)

Verified step by step guidance

1. Understand that an atom consists mostly of empty space, with a tiny, dense nucleus at its center.
2. Recall that the size of the nucleus is on the order of 1 femtometer (1 \times 10^{-15} meters), while the size of the entire atom is on the order of 0.1 nanometers (1 \times 10^{-10} meters).
3. Calculate the volume of the nucleus using the formula for the volume of a sphere: \(V = \frac{4}{3} \pi r^3\), where \(r\) is the radius of the nucleus.
4. Calculate the volume of the atom using the same volume formula but with the atomic radius.
5. Compare the two volumes by dividing the nucleus volume by the atom volume and multiply by 100 to get the percentage of the atom's volume occupied by the nucleus.