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.

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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.

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