If the radius of a neutron is 1.0*10-13cm, calculate the density of a neutron in g/cm3. (volume of a sphere = 43πr3) Express your answer using two significant figures. ρ If you need this result for any later calculation in this item, keep all the digits and round as the final step before submitting your answer. Assuming that a neutron star has the same density as a neutron, calculate the mass in kilograms of a small piece of a neutron star the size of a spherical pebble with a radius of 0.30 mm. Express your answer using two significant figures.

Answers

part 1

Density of a substance is the ratio of mass of a unit volume of that substance.

Density = mass/volume

volume of a sphere = 4/3 * πr³

Volume of the neutron = 4/3 * π * (1*10⁻¹³) ³

= 4.18879 * 10⁻³⁹ cm³

mass of a neutron = 1.674929 x 10⁻²⁷ kg

= 1.674929 x 10⁻²⁴ g

density = (1.674929 x 10⁻²⁴) / (4.18879 * 10⁻³⁹)

= 3.999 * 10¹⁴ g/cm³

Answer to 2 significant figures = 4.0 * 10¹⁴ g/cm³

Part 2

density of neutron star = 4.0 * 10¹⁴ g/cm³

Radius = 0.30 mm = 0.03 cm

volume = 4/3 * π * 0.03³

= 1.13097 * 10⁻⁴ cm³

mass = density * volume

= 4.0 * 10¹⁴ * 1.13097 * 10⁻⁴

= 4.52388 * 10¹⁰ g

Answer to 2 significant figure = 4.5 * 10¹⁰ g