Question

Assume the average density of the universe is 0.1 of the critical density needed for closure. What is the average number of protons per cubic meter, assuming the universe is composed mostly of hydrogen?

a) 1.67×10⁻²⁴
b) 1.67×10⁻²⁷
c) 1.67×10⁻³⁰
d) 1.67×10⁻³³

Answer 1

The average number of protons per cubic meter in the universe, given that its average density is 0.1 of the critical density and the universe is mostly hydrogen, is 1.67×10-27, corresponding to one proton per cubic meter. Option b is the correct answer.

Step-by-step explanation:

The question pertains to the average density of the universe and its relationship to the critical density needed to halt the expansion of the universe, as well as the derivation of the average number of protons per cubic meter from this density, assuming the universe is mostly composed of hydrogen.

The critical density (ρcrit) of the universe is approximately 10-26 kg/m³. If the actual average density of the universe is about 0.1 of this critical density, we have an average density of 10-27 kg/m³. Considering that hydrogen is mostly composed of protons and each proton has a mass of about 1.67 × 10-27 kg, there would be approximately one proton per cubic meter, which leads us to answer (b) 1.67×10-27.