Assuming that a neutron star is as dense as an atomic nucleus,estimate the number of nucleons in a 10 km diameter star.

Question

Quizplus · Accepted Answer

The density of an atomic nucleus is roughly $2.3 \times 10^{17} \, \text{kg/m}^3$. The volume of a sphere is given by $\frac{4}{3}\pi r^3$, where $r$ is the radius. For a neutron star with a 10 km diameter, the radius is 5 km or $5000 \, \text{m}$. Thus, the volume is $\frac{4}{3}\pi (5000)^3 \, \text{m}^3$. Multiplying this volume by the density gives the mass of the neutron star. The mass of a nucleon is approximately $1.67 \times 10^{-27} \, \text{kg}$. Dividing the total mass by the mass of a single nucleon gives the total number of nucleons, which is approximately $8.9 \times 10^{55}$, matching choice C.

Assuming That a Neutron Star Is as Dense as an Atomic