Consider a white dwarf, a neutron star and a black hole, all with equal masses of 1.4 times the mass of the Sun. If the density in the neutron star is 1015 g cm-3, what is its radius?
A very good question!!. Now let us see.
The mass of our sun is about: 2 X 10^33 Grams. Therefore the mass of the neutron star is
1.4 X 2 X 10^33=2.8 X 10^33 Grams
Now, Density=mass/volume, therefore.
10^15=2.8 X10^33/volume, we have,
Volume=2.8 X 10^33/ 10^15
Volume=2.8 X 10^18 cubic cm. Now, the volume of a sphere is: 4/3PiR^3, therefore we have
2.8 X 10^18=4/3PiR^3
.................. =4/3*3.14159265358*R^3
...................=4.1887902047733*R^3, therefore,
R^3=(2.8 X10^18) / 4.18879047733,
R^3=6.6845 X 10^17,
R=(6.6845 X 10^17)^1/3
R=874,359cm, or, 8743.59 meters, or,
R=8.74359 Km, being the radius of the neutron star.
