One theory of the universe\'s origin states that a very early time it had a dens

Question

One theory of the universe's origin states that a very early time it had a density of about 1.518x10^15 g/cm^3 and a radius approximately equal to the average distance from the sun to the earth. This average value defines an astronomical Unit (AU). The value can be easily looked up . Consider the moment when the assumed spherical homogeneous early universe had the density d and had a radius of 1.32 AU. If the only particles making up the universe then were in the proportions 1/3 protons, 1/3 neutrons and 1/3 electrons, how many particles were in the universe? Take the combined mass of one set of these 3 particles to be 3.35x10^-24 g

Explanation / Answer

One AU 149597870700 metres

so,

r = 1.32 au = 1.97469 * 10^11 m

volume = (4/3)*pi*r^3

mass = density * volume = 48.9610 * 10^54 g

mass of 1 set = 3.35x10^-24 g

so, number of sets = 48.9610 * 10^54 g / (3.35x10^-24 g)

= 14.6152 * 10^78 sets

so, number of particles = 3 * number of sets

number of particles = 4.38457 * 10^79 particles

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