The diameter of an atom is 1.4 × 10^-10 m and the diameter of its nucleus is 1.0 × 10^-14 m.What fraction of the atom's volume is occupied by its nucleus? A)3.6 × 10^-13 B)7.1 × 10^-5 C)5.1 × 10^-9 D)2.6 × 10^-17

Question

Quizplus · Accepted Answer

The volume of a sphere is given by $V = \frac{4}{3}\pi r^3$, where $r$ is the radius. The radius of the atom is $0.7 \times 10^{-10}$ m, and the radius of the nucleus is $0.5 \times 10^{-14}$ m. The volume of the atom is $\frac{4}{3}\pi (0.7 \times 10^{-10})^3$ and the volume of the nucleus is $\frac{4}{3}\pi (0.5 \times 10^{-14})^3$. The fraction of the atom's volume occupied by its nucleus is the ratio of the nucleus's volume to the atom's volume, which simplifies to $\left(\frac{0.5 \times 10^{-14}}{0.7 \times 10^{-10}}\right)^3 = \left(\frac{1}{14}\right)^3 = \frac{1}{2744} \approx 3.6 \times 10^{-13}$, making choice A correct.

The Diameter of an Atom Is 1