This entry was posted on May 10, 2022 by Anne Helmenstine (updated on November 19, 2023)
Have you ever wondered how many atoms are in the world? You can guess it’s a gigantic number, but just how big is it? Here is the approximate answer to the question and a look at how you calculate it.
Number of Atoms in the World
The number of atoms in the world is around 1.3 x 1050.
Here is the number written out:
130,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
That’s a lot of atoms! The number is an approximation because its calculation requires making estimates about the mass and composition of the Earth and also because the number of atoms is always changing. The Earth loses atoms as they escape the atmosphere. It gains atoms from meteors and other matter coming in from space.
How to Calculate the Number of Atoms in the World
Find the Mass of the Earth
The first step in finding the number of atoms in the world is finding the mass of Earth. We know the mass of the Earth is around 5.98 x 1027 grams. This comes from knowing the diameter of the planet and the acceleration due to gravity. This gives us an average density of the Earth (5515kg/m3). Density is mass per unit of volume. Volume comes from assuming the Earth is more or less a sphere (even though it’s more of a lumpy ellipsoid). Mass is the density multiplied by the volume. Scientists have known the mass of the world since the 1770s. While it’s an estimate, it’s known with a fair degree of certainty.
Find the Composition of the Earth
The next step is determining the elemental composition of the Earth because each type of atom has a different mass. So, if the world only contained iron atoms it would have fewer atoms than if it only contained hydrogen atoms. This is because iron atoms have more mass than hydrogen atoms.
We have an idea of the composition of the Earth, but don’t know the details about what’s going on in the planet’s core with certainty. Our present understanding indicates the Earth is about 32.1% iron, 30.1% oxygen, 15.1% silicon, 13.9% magnesium, 2.9% sulfur, 1.8% nickel, 1.5% calcium, 1.4% aluminum, and 1.2% amounts other elements. This assumes a core that is mostly iron (88.8%), with smaller amounts of nickel (5.8%), sulfur (4.5%), and less than 1% other elements.
Find the Mass of Each Element
From the periodic table, the relative atomic masses of these elements are: iron (55.8 g/mol), oxygen (16.0 g/mol), silicon (28.1 g/mol), magnesium (24.3 g/mol), sulfur (32.1 g/mol), nickel (58.7 g/mol), calcium (40.1 g/mol), and aluminum (27.0 g/mol).
Next, multiply the mass fraction by the total mass of the Earth to get the mass in grams for each element. For example, the grams of oxygen in the world is 0.301 x 5.98 x 1027 grams = 1.80×1027 grams.
<!-MONUMETRIC Repeatable 2 D:300x250 T:300x250 M:300x250,320x50 START->
<!-MONUMETRIC Repeatable 2 D:300x250 T:300x250 M:300x250,320x50 ENDS->
Find the Number of Moles of Each Element
Find the number of moles of each element using the mass in grams and the atomic mass of each element.
moles of element = grams of element / atomic mass
For example, the number of moles of iron is:
moles iron = 1.92×1027 g / 55.8 g/mol = 3.44×1025
Find the Numbers of Atoms of Each Element
Finally, find the number of atoms of each element. The number of atoms of iron is Avogadro’s number divided by the number of moles.
atoms of iron = 6.022×1023 atoms/mol x 3.44×1025 mol = 2.07×1049
Putting it all together gives us the mass of the world:
| Element | Grams per mole | Mass Fraction | Amount in Grams | Number of Atoms |
|---|---|---|---|---|
| Iron | 55.8 | 0.321 | 1.92×1027 | 2.07×1049 |
| Oxygen | 16.0 | 0.301 | 1.80×1027 | 6.77×1049 |
| Silicon | 28.1 | 0.151 | 9.03×1026 | 1.94×1049 |
| Magnesium | 24.3 | 0.139 | 8.31×1026 | 2.06×1049 |
| Sulfur | 32.1 | 0.029 | 1.73×1026 | 3.25×1048 |
| Nickel | 58.7 | 0.018 | 1.08×1026 | 1.11×1048 |
| Calcium | 40.1 | 0.015 | 8.97×1025 | 1.35×1048 |
| Aluminum | 27.0 | 0.014 | 8.37×1025 | 1.87×1048 |
This accounts 98.8% of the Earth’s mass, which is a decent approximation. The number of atoms in the world is the sum of the number of atoms of each element, which is around 1.35×1050 atoms.
Comparing Atoms in the Earth to Way of Arranging a Deck of Cards
So, 1050 is an impossibly large number, but in the grand scheme of things, it might be smaller than you think. For example, do you think there are more atoms in the world than there are ways of ordering a regular deck of playing cards?
There are 52 cards in a deck. The number of different ways you can order these cards is 52! or 52 factorial. Factorials get big quickly. For example:
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040
52! is an incomprehensibly huge number:
52! = 52 x 51 x 50 … which is approximately 8.0658 x 1067
So, there are (a lot) more ways of ordering the cards in a deck than there are atoms in the world!
References
- Morgan, J. W.; Anders, E. (1980). “Chemical composition of Earth, Venus, and Mercury”. Proceedings of the National Academy of Sciences. 77 (12): 6973–77. doi:10.1073/pnas.77.12.6973
- Müller, Edith A.; Jappel, A., eds. (1977), “IAU (1976): Proceedings of the 16th General Assembly, XVI B”. Transactions of the IAU. Dordrecht: D. Reidel. ISBN 90-277-0836-3.
- Ries, J.C.; Eanes, R.J.; Shum, C.K.; Watkins, M.M. (1992). “Progress in the determination of the gravitational coefficient of the Earth”. Geophysical Research Letters. 19 (6): 529. doi:10.1029/92GL00259
- Schlamminger, Stephan (18 June 2014). “Fundamental constants: A cool way to measure big G”. Nature. 510 (7506): 478–480. doi:10.1038/nature13507
