Certain stars are thought to collapse at the end of their lives, combining their protons and electrons to form a neutron star. Such a star could be thought of as a giant atomic nucleus. If a star with a mass equal to that of the sun (of mass 1.99 × 1030 kg) were to collapse into neutrons, what would be the radius of the star? Answer in units of m.
Thank you for the opportunity to help you with your question!
If we assume the inter neutron space is s = 1E-35 m (a Planck Length) and all the 1.99E30 kg were somehow all neutrons, we'd have N = M/n = 1.99E30/1.67E-27 = 1.19162E+57 neutrons would be crammed into a volume V = 4/3 pi R^2; where R = sqrt(V/(4/3 pi)) = ? meters. n = 1.67E-27 kg is the rest mass of a neutron.
As an approximation to the volume each neutron takes up, we assume v = s^3 = 1E-105 m^3, that is, the Plank Length cubed. So V = Nv = 1.19E57 * 1E-105 = 1.19E-48 m^3.
Then R = sqrt(1.19E-48/((4/3)*pi())) = 5.33002E-25 m.
Please let me know if you need any clarification. I'm always happy to answer your questions.