Question

A proton, which is the nudleus of a hydrogen atom, can be modeled as a sphere with a diameter of 2.4 fm and a mass of 1.67 x 1027 kg. Deusities of Some Common Substances at Standard Temperature (0'C) and Pressure (Atmospheric Substance Air Air (at 20 Cand P (kg/m Substance p (kg/m 786 × 10 11.3 × 10° 13,6 x10° 1.25 0.710 x 10 22.6 × 10- 1.43 0.373 × 10° 214 x 10 1.08 x 10 10.5 x 10 7.30 × 10- 19.1 x 10s Iron Lead Mercury Nitrogen gas Oak Osmium 1.29 atmospheric pressure) Aluminum Benzene Brass Copper Ethyl alcoho Fresh water Glycerin Gold Helium gas Hydrogen gas Ice 1.20 270 × 10, 0.879 × 10° 8.4 105 8.92 x 10xgen gas 0.806 × 105 1.00 × 105 1.26 x 10 19.3× 105 1.79 × 10-1 Pine Platinum Seawater Silver Tin 8.99 × 10-2 0.917 × 10, Uranium (a) Determine the density of the proton. kg/m (b) State how your answer to part (a) compares with the density of siliver, given the table above. less than silver equal to silver greater than silver

Answer 1

Solution

a ) Radius of the proton = r = 2.4/2 fm = 1.2 x 10^-15 m

( 1 fm = 10^-15 m)

Volume = 4/3 pi r^3 = 4/3 pi * (1.2 × 10^-15)^3 = 7.24 x 10^-45 m^3

Mass of the proton = 1.67 x 10 ^-27 kg

Density of the proton = mass / volume

= ( 1.67 x 10^-27 ) / (7.24 × 10 ^-45)

= 2.31 x 10^17 kg/m^3

b) density of proton is Greater than the density of silver.