There is a joke that says, ‘do not trust atoms, they make up everything.’ So how many atoms are there in the universe? There are two methods that can be used to get the answer to this question.
One of them considers what is called the Cosmic Microwave Background radiation (this is a remnant of the big bang) this one assumes the cosmological principle to be true. The principle states that from large scale observations, the property of the physical universe should be the same. That is to say that the universe is homogeneous.
This calculation is a mathematical nightmare that am not going to tackle. I will instead use the second method to estimate the number of atoms in the universe by calculation of mass.
A few facts to consider.
Before we dive deep, there are a few facts that are important to consider first for this to make sense. When we calculate the number of atoms we are actually calculating the number of atoms in the observable universe alone. This observable universe has radius of 300 million light years in any direction that is 2.83824 X 1018 Km. For all we know, the universe may be infinite and as such may have an infinite number of atoms.
Second fact is that hydrogen makes up slightly less than 75% of all the atoms in the universe. And Helium makes up slightly below 25% of all atoms. All other elements make up less than 1% of the atoms in the universe. Remember that the difference in the hydrogen and helium atom is actually a single electron.
Fact number three is that 99.99999999999996% of a hydrogen atom is made up of empty space. Therefore it is safe to make the assumption that the entire mass of a hydrogen atom is derived from the proton.
All atoms are hydrogen atoms in the universe are hydrogen atoms (the assumption is based of the two latter facts).
Fact 4 is based on the principle of gravitation. As we make observations we see that matter in our universe tend to form in a hierarchical manner; atoms condense in to stars, in return stars form galaxies, galaxies form clusters, clusters form super clusters and super-clusters form even larger structure.
The assumption here is that all the matter in the universe is condensed in to galaxies.
The mass of an average star (sun sized star) is 1035g
An average galaxy has about 400 billion stars; 4X1011 stars.
The observable universe has about 300 billion galaxies 3X1011 galaxies
1 gram of matter has 1024 protons (hydrogen without the electrons)
The number of atoms is (1035 X 1024 X 12 X 1022)
The actual value is 1082 protons. So if I could refine the assumption, I could get the same result.
The value from the cosmic microwave background radiation gives a value of 1X1078 protons.
The number of atoms in the universe is between 1070 and 1082 atoms. That is between ten quadrillion vigintillion and one hundred thousand quadrillion vigintillion.
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the picture of the galaxy was obtained from here. I hold no rights about its usage.