Problem: Neutron stars are believed to be composed of solid nuclear matter, primarily neutrons. Assuming that a neutron star has the same density as a neutron  (density = 4.0×1014 g/cm3), calculate the mass (in kg) of a small piece of a neutron star the size of a spherical pebble with a radius of 0.16 mm .

FREE Expert Solution

Recall that density is the ratio of the mass and volume of an object:

$\boxed{\mathbf{density}\mathbf{=}\frac{\mathbf{mass}}{\mathbf{volume}}}$

Also, the volume of a sphere is given by:

$\boxed{\mathbf{V}\mathbf{=}\frac{\mathbf{4}}{\mathbf{3}}{\mathbf{\pi r}}^{\mathbf{3}}}$

$\mathbf{V}\mathbf{=}\frac{\mathbf{4}}{\mathbf{3}}\mathbf{\pi }{\mathbf{(}\mathbf{0}\mathbf{.}\mathbf{16}\mathbf{ }\cancel{\mathbf{mm}}\mathbf{\times }\frac{\mathbf{1}\mathbf{ }\mathbf{cm}}{\mathbf{10}\mathbf{ }\cancel{\mathbf{mm}}}\mathbf{)}}^{\mathbf{3}}$

V = 1.716 x 10^-5 cm³