Number of Atoms in Observable Universe

Theorem
The number of atoms in the observable universe is approximately $10^{80}$.

Proof
According to our current observations and understanding of the, the age of the universe is estimated to be $13.787$ billion years.

That means the light from the most distant galaxies has traveled $13.787$ billion years to reach us.

The speed of light is $299 \, 792 \, 458 \ \text {m s}^{-1}$

This implies that the radius of the observable universe (assuming no expansion) is:

However, contemplating expansion at an average rate of $8.8 \%$ per billion years, we obtain:

This in turn implies that the volume of the observable universe is:

Finally, assuming there is approximately $1$ atom per cubic metre brings us to our estimate of approximately $10^{80}$ atoms in the observable universe.