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? A) 3.6 × 10^-13 cm B) 2.0 × 10^-37 cm C) 4.8 × 10^-38 cm D) 2.2 × 10^-19 cm E) None of these choices are correct.

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 correct answer is A.

If the Density of a Certain Spherical Atomic Nucleus Is