The proton has a radius of approx 1.0 x 10 to -13 power cm and a mass of 1.7 x 10 to -24 power g. Determine the desity of a proton. For a sphere

Question

The proton has a radius of approx. 1.0 x 10 -13 power cm and a mass of 1.7 x 10 x -24 power g.  Determine the density of a proton.  For a sphere  v=(4/3) x pi cubed

Answer 1

This is a 2-part algebraic problem relating to mass/density/volume and the volume of a sphere.

 

Proton's radius (Rp) = 1.0 x (10^-13) cm = (1/100) x (10^-13) m = 1.0 x (10^-15) m

Proton's mass (Mp) = 1.7 x (10^-24) g = (1.7/1000) x (10^-24) kg = 1.7 x (10^-27) kg

Proton's volume (Vp) = (4/3)pi(r^3)

 

Density (Dp) = mass (Mp) / volume (Vp)

Dp = Mp/Vp = Mp / (4/3)pi(Rp^3) = (3*Mp) / (4pi(Rp^3))

Dp = 3(1.7 x (10^-24) g) / [4pi(1.0 x (10^-13)) cm^3]

Dp =  4.05845105 x (10^-12) g/(cm^3)

 

If you needed to give your answer in units of meters/kilograms cubed (m/kg^3), then

Dp = 4.05845105 x (10^-13) kg/(m^3)