#### Question

A neutron star has a density equal to that of the nuclear matter. Assuming the star to be spherical, find the radius of a neutron star whose mass is 4.0 × 10^{30} kg (twice the mass of the sun).

#### Solution

Given:

Mass of the neutron star, M = 4.0 × 10^{30} kg

Density of nucleus , d = `2.4 xx 10^17`

Density of nucleus, d= `M/V`

Here, V is the volume of the nucleus.

`therefore V = M/d = (4 xx 10^30)/(2.4 xx 10^17)`

= `1/0.6 xx 10^13`

= `1/6 xx 10^14`

If R is the radius, then the volume of the neutron star is given by

`V = 4/3piR^3`

`therefore 1/6 xx 10^14 = 4/3 xx pi xx R^3`

⇒ `R^3 = 1/6 xx 3/4 xx 1/pi xx 10^14`

⇒ `R^3 = 1/8 xx 100/pi xx 10^12`

`therefore R = 1/2 xx 10^4 xx 3.17`

= `1.585 xx 10^4 = 15 "km"`

Is there an error in this question or solution?

Solution A Neutron Star Has a Density Equal to that of the Nuclear Matter. Assuming the Star to Be Spherical, Find the Radius of a Neutron Star Whose Concept: Mass-energy and Nuclear Binding Energy - Mass - Energy.