# How many atoms are in the universe?

## Make the following assumptions: (a) Assume that all of the atoms in the universe are hydrogen atoms in stars. (b) Assume that the sun is a typical star composed of pure hydrogen with a density of 1.4g/cm^3 and a radius of 7*10^8m . (c) Assume that each of the roughly 100 billion stars in the Milky Way galaxy contains the same number of atoms as our sun. (d) Assume that each of the 10 billion galaxies in the visible universe contains the same number of atoms as our Milky Way galaxy

Aug 20, 2016

Under the given assumptions
(a) Assume that all of the atoms in the universe are hydrogen atoms in stars.
(b) Assume that the sun is a typical star composed of pure hydrogen with a density of $1.4 g c {m}^{-} 3$ and a radius of $7 \times {10}^{8} m$.
(c) Assume that each of the roughly 100 billion stars in the Milky Way galaxy contains the same number of atoms as our sun.
(d) Assume that each of the 10 billion galaxies in the visible universe contains the same number of atoms as our Milky Way galaxy

Using CGS units

Mass of sun$= \text{Density"xx"Volume}$
Inserting given values we obtain
Mass of sun$= 1.4 \times \frac{4}{3} \pi {\left(7 \times {10}^{10}\right)}^{3} = 2.011 \times {10}^{33} g$
Average atomic mass of hydrogen atom$= 1.008 a m u$
Avogadro's number $6.02 \times {10}^{23}$ of atoms in $1$ mole of Hydrogen

Number of Hydrogen atoms in our sun$= \text{Mass of sun"/"Molar mass of Hydrogen atom"xx"Avogadro's number}$
$= \frac{2.011 \times {10}^{33}}{1.008} \times 6.02 \times {10}^{23} = 1.201 \times {10}^{57}$
Number of atoms in our milky way galaxy$= \text{Number of stars"xx"Number of atoms in sun}$
$= 1.00 \times {10}^{11} \times 1.201 \times {10}^{57}$
$= 1.201 \times {10}^{68}$

Number of atoms in observable universe$= \text{Number of galaxies"xx"Number of atoms in our galaxy}$
$= 1.00 \times {10}^{11} \times 1.201 \times {10}^{68}$
$= 1.201 \times {10}^{79}$