If the density of a certain spherical atomic nucleus is 1.0 × 10¹⁴ g cm^-3 and its mass is 2.0 × 10^-23 g, what is its radius in cm?

Question

Quizplus · Accepted Answer

The density of a sphere is given by the formula:$$ ho = \frac{3M}{4\pi r^3}$$where $ ho$ is the density, $M$ is the mass, and $r$ is the radius.We can rearrange this formula to solve for the radius:$$r = \sqrt[3]{\frac{3M}{4\pi ho}}$$Plugging in the given values, we get:$$r = \sqrt[3]{\frac{3(2.0 imes 10^{-23} ext{ g})}{4\pi (1.0 imes 10^{14} ext{ g cm}^{-3})}} = 3.6 imes 10^{-13} ext{ cm}$$Therefore, the radius of the nucleus is 3.6 × 10^-13 cm.

If the Density of a Certain Spherical Atomic Nucleus Is