The volume of a carbon atom is 1.9 × 10^-30 m³.What is the radius of the atom in picometers? The volume of a sphere is (4/3)πr³.

Question

Quizplus · Accepted Answer

Given the volume of the carbon atom is $1.9 \times 10^{-30} m^3$, we can use the formula for the volume of a sphere, $V = \frac{4}{3}\pi r^3$, to find the radius. Rearranging the formula to solve for $r$, we get $r = \left(\frac{3V}{4\pi}\right)^{\frac{1}{3}}$. Substituting $V = 1.9 \times 10^{-30} m^3$ into the formula, we find the radius in meters. To convert meters to picometers ($1 m = 10^{12} pm$), we multiply the radius in meters by $10^{12}$. Doing the math, we find that the radius is approximately 77 picometers.

The Volume of a Carbon Atom Is 1