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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.

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smmwaite

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

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