The Big Bang theory postulates that the entire presently known universe, shortly after the Big Bang, was approximately 1 AU in radius (1.5 × 1011 m) and had a mass density of 1015 g/cm3. If we assume that one part of this sphere was composed of protons, one part of neutrons, and one part of electrons, how many particles were contained in the universe at that time? (Protons and neutrons each have a mass of 1.67 × 10−30 g. An electron has a mass of 9.11 × 10−33 g.) . we are given the radius of the universe shortly after the big bang: converted to centimeters it is 1.5 × 1013 cm. the volume of a sphere is 0.75 × π × r3