When you look up the atomic mass of an element, say carbon, you go to the periodic table and look under the element symbol. This value is actually the average atomic mass of the element. But, average of what?

Most naturally occurring elements have more than one isotope. **Isotopes** of an element have different masses because they contain different numbers of neutrons. When measuring the atomic mass, scientists settle on using the *average* mass of the naturally occurring mixture of isotopes.

## Calculating the Average Atomic Mass

Take a look at carbon: The natural abundance of carbon-12 and carbon-13 are 98.90 percent and 1.10 percent respectively. The atomic mass of carbon-12 is 12.00000 amu (atomic mass unit) while the atomic mass of carbon-13 is 13.00335 amu.

In order to calculate the average atomic mass, the percentage abundance must first be converted to decimals. The means that when added together, the abundances must equal one. To convert the percent abundance to a decimal, divide by 100.

The fractional abundance of carbon-12 is 0.9890, and the fractional abundance of carbon-13 is 0.0110.

Next, you multiply the fractional abundance by the mass and add them together.

So,

The average atomic mass of carbon is this 12.01 amu. This is the number reported on the periodic table. It makes sense that the average atomic mass is closer to 12 since the fractional abundance of carbon-12 is much more than carbon-13.

## The Average Atomic Mass Formula

The process above can be generalized with the following formula:

Here, *m* is the mass of a specific isotope, and *f* is the fractional abundance. As long as all values of *f* add up to one, you're good to go. This is a good check to make sure you are doing the math correctly.

Take a look at this example of calculating the average atomic mass of magnesium. The table below contains information about the isotope, mass and abundance.

Isotope | Mass | Abundance |
---|---|---|

| 23.98504 | 78.99% |

| 24.98583 | 10.00% |

| 25.98259 | 11.01% |

You can make use of the formula above to find the average atomic mass.

Begin by converting the percentages to fractional abundance by dividing each number by 100. After doing this the table looks as follows:

Isotope | Mass | Fractional Abundance |
---|---|---|

| 23.98504 | 0.7899 |

| 24.98583 | 0.1000 |

| 25.98259 | 0.1101 |

In order to make sure that you have done the math correctly and that the values you have are correct, it is a good idea to make sure that all the fractional abundances add up to one.

Good, it adds up to one. You can continue with the calculation.

Next, you can plug in the mass and corresponding fractional abundance into the equation described above:

Putting in the values from the table yields:

Together this means that the average atomic mass of Mg is:

It is very important to note that while the average atomic mass of magnesium is 24.31 amu, and the average atomic mass of carbon is 12.01 amu, this is not the mass of any individual atom. For example, if you were to pick up an **individual carbon atom** (pretend that's possible!) then it would either be 12.00 amu or 13.000335 amu. It would *not* be 12.01 amu.

In the same way when you pick up any individual magnesium atom it would either be 23.98504 amu, 24.98583 amu or 25.98259 amu. The average atomic mass is simply a way for scientists to account for the stable isotopes of an element that exist on earth. It does not denote the mass of an individual atom unless that element only has one stable isotope.

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About the Author

Riti Gupta holds a Honors Bachelors degree in Biochemistry from the University of Oregon and a PhD in biology from Johns Hopkins University. She has an interest in astrobiology and manned spaceflight. She has over 10 years of biology research experience in academia. She currently teaches classes in biochemistry, biology, biophysics, astrobiology, as well as high school AP Biology and Chemistry test prep.