If the sun collapsed to a neutron star, what would its radius be?

[sammyz]

Homework Statement

Suppose the sun collapses into a neutron star. What will its radius be? The questions also gives some backround explaining that stars fuse hydrogen into helium until they collapse into a neutron star. The protons and electrons fuse into neutrons with the density of nuclear matter.

Homework Equations

The Attempt at a Solution

I'm not sure exactly how to begin. I am assuming I am supposed to use the number for the density of nuclear matter which is 2.3 * 10^17 kg/m^3 but I do not know where to go from here. It would be nice to just get a hint. Thanks.

 

[Kurdt]

What you must assume is that the wntire mass of the sun gets condensed into an extrememly dense neutron core. You are given the density of a neutron star and thus it is easy to relate the mass to the volume and thus the radius as you assume the sun will condense into a sphere.

$$\rho_{core} = \frac{m_{sun}}{\frac{4}{3}\pi r^3}$$