The mass of the Sun is \(2 \cdot 10^{30} \mathrm{~kg}\), and the Sun contains more than \(99 \%\) of all the mass in the solar system. Astronomers estimate there are approximately 100 billion stars in the Milky Way and approximately 100 billion galaxies in the universe. The Sun and other stars are predominantly composed of hydrogen; a hydrogen atom has a mass of approximately \(2 \cdot 10^{-27} \mathrm{~kg}\). a) Assuming that the Sun is an average star and the Milky Way is an average galaxy, what is the total mass of the universe? b) Since the universe consists mainly of hydrogen, can you estimate the total number of atoms in the universe?

Given the mass of the Sun (\(2 \cdot 10^{30} \mathrm{~kg}\)), and the number of stars in a galaxy (100 billion) and the number of galaxies (100 billion), we can assume that the Sun is an average star and the Milky Way is an average galaxy. To find the total mass of the universe, we can multiply the mass of the Sun by the number of stars in a galaxy, and then multiply this by the number of galaxies in the universe: Total mass of the universe = Mass of the Sun x Number of stars in a galaxy x Number of galaxies in the universe Total mass of the universe = \((2 \cdot 10^{30} \mathrm{~kg}) \times (100 \times 10^9) \times (100 \times 10^9)\) Total mass of the universe = \(2 \cdot 10^{30} \times 10^{20} \mathrm{~kg}\) The total mass of the universe is approximately \(2 \cdot 10^{50} \mathrm{~kg}\).

Since the universe consists mainly of hydrogen and we are given the mass of a hydrogen atom, we can estimate the total number of hydrogen atoms in the universe by dividing the total mass of the universe by the mass of a hydrogen atom: Total number of hydrogen atoms in the universe = Total mass of the universe / Mass of a hydrogen atom Total number of hydrogen atoms in the universe = \((2 \cdot 10^{50} \mathrm{~kg}) / (2 \cdot 10^{-27} \mathrm{~kg})\) Total number of hydrogen atoms in the universe = \(10^{77}\) So the universe contains approximately \(10^{77}\) hydrogen atoms.