Final answer:
The question involves calculating the density of an atomic nucleus, estimated to be roughly 10¹⁸ kg/m³, and the radius of a neutron star with 10 times the mass of our Sun. The atomic nucleus density is found by recognizing that the volume of a nucleus is substantially smaller than that of the entire atom, while maintaining nearly all of its mass. For the neutron star, complex astrophysical calculations are required, involving the volume and mass relationship of a sphere and the density of a nucleus.
Step-by-step explanation:
Estimating the Density of a Nucleus and Calculating Neutron Star Radius
The question tackles two distinct physical concepts related to density and it can be split into two different parts:
- Density of an atomic nucleus: Given that the average density of an atom is approximately 10³ kg/m³ and the nucleus has a radius about 10⁻⁵ that of the atom, we can estimate the density of the nucleus by considering the volume it occupies. Since the mass is nearly the same but the volume is significantly smaller (about 10¹⁵ times), the density of an atom's nucleus is estimated to be on the order of 10¹⁸ times greater than the average atomic density, leading to an approximate density of 10¹⁸ kg/m³.
- Radius of a neutron star: A neutron star is the remnant of a supernova and its density is comparable to that of an atomic nucleus. To calculate the radius of a neutron star with a mass 10 times that of our Sun, we can use the formula for the volume of a sphere and the known density of a nucleus. However, we will need to assume certain conditions and use some simplifications to give an approximate answer since an exact calculation would require complex astrophysics.
These problems involve principles from nuclear physics and astrophysics and serve as good examples of applying our understanding of atomic structure to cosmic entities.