# Average Atomic Mass | Definition, History, Examples

## Definition of Average Atomic Mass

Average atomic mass considers the isotopic abundance (relative to each other found in the Earth).

For example, the most abundant carbon isotope is carbon-12, which has a relative abundance of 98.89%. The atomic masses of carbon-13 and carbon-14 are 13.003 amu and 14.003 amu, respectively. The average atomic mass of carbon is 12.011 amu.

• Have you ever gone through a whole bag of multi-colored M&Ms? If you look inside the bag of M&M’s, the shape and size of each M&M are relatively the same. However, there are different colors, so we can say that they have different versions. If we count how many M&Ms there are for each color, sometimes we find that the most popular color in one bag is brown, and the other times, it is green or yellow.
• Have you ever wondered how pennies have changed over the years? The penny has undergone several design changes and composition changes. Some pennies are made purely of copper, some of nickel, tin, and zinc. If we find the masses of pennies from different years, their masses are different because their composition is different. In 1793, the penny’s mass was 13.48 g, and now, it is only 2.5 g.

Just like M&Ms and pennies have different versions, atoms of the elements in the periodic table have different versions of each other called isotopes. Isotopes are different versions of the same elements with different numbers of neutrons and different atomic masses.

### Other Definitions

1. Average atomic mass of an element refers to the atomic masses of the isotopes of the element, taking into account the different abundances of the element’s isotopes. An element can have differing neutrons in its nucleus, but it always has the same number of protons. The versions of an element with different neutrons have different masses and are called isotopes.
2. The average atomic mass for an element is calculated by summing the masses of the element’s isotopes, each multiplied by its natural abundance on Earth.
3. When doing any mass calculations involving elements or compounds, always use average atomic mass, which can be found on the periodic table.
4. The mass calculated by summing the masses of an element’s isotopes, each multiplied by its natural abundance on Earth.

## History

The first scientists to determine relative atomic masses were John Dalton and Thomas Thomson between 1803 and 1805 and Jon’s Jakob Berzelius between 1808 and 1826.

Relative atomic mass (Atomic weight) was initially defined relative to that of the lightest element, hydrogen, which was taken as 1.00. In the 1820s, Prout’s hypothesis stated that atomic masses of all elements would prove to be exact multiples of that of hydrogen.

However, Berzelius soon proved that this was not even approximately true. And for some elements, such as chlorine, relative atomic mass, at about 35.5, falls almost halfway between two integral multiples of that of hydrogen. Still later, this was shown to be largely due to a mix of isotopes and that the atomic masses of pure isotopes, or nuclides, are multiples of the hydrogen mass, to within about 1%.

In the 1860s, Stanislao Cannizzaro refined relative atomic masses by applying Avogadro’s law (notably at the Karlsruhe Congress of 1860). He formulated a law to determine relative atomic masses of elements. The different quantities of the same elements contained in other molecules are all whole multiples of the atomic weight and determined relative atomic masses and molecular masses by comparing the vapor density of a collection of gases with molecules containing one or more of the chemical element in question.

## Calculating Average Atomic Mass

• The average atomic mass can be calculated using the following formula. Average Atomic Mass = (Mass of isotope x % natural abundance) / 100.
• The average atomic mass of an element is the sum of the masses of its isotopes, each multiplied by its natural abundance (the decimal associated with percent of atoms of that element that are of a given isotope).
• Average atomic mass = f1 M1 + f2 M2 + … + fn Mn where f is the fraction representing the natural abundance of the isotope and M is the mass number (weight) of the isotope.
• The average atomic mass of an element can be found on the periodic table, typically under the elemental symbol. When data are available regarding the natural abundance of various isotopes of an element. It is simple to calculate the average mass.
• To calculate the average mass, first convert the percentages into fractions (divide them by 100). Then, calculate the mass numbers. The chlorine isotope with 18 neutrons has an abundance of 0.7577 and a mass number of 35 amu. To calculate the average atomic mass, multiply the fraction by the mass number for each isotope, then add them together.

## Examples of Average Atomic Mass

1. For helium, there is approximately one isotope of Helium-3 for every million isotopes of Helium-4; therefore, the average atomic mass is very close to 4 amu (4.002602 amu).
2. Chlorine consists of two major isotopes, one with 18 neutrons and the other with 20 neutrons. The atomic number of chlorine is 17 (it has 17 protons in its nucleus).