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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 × 1030 kg (twice the mass of the sun).
Solution
Given:
Mass of the neutron star, M = 4.0 × 1030 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"`
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