*Felicia Fullilove*

# Atomic Mass Unit (AMU): Definition, Standard & Conversion

## What Is an Atom?

How much do you weigh? No need to answer out loud, but whatever the answer, I am sure the amount was expressed in pounds or kilograms. What are you made of? You may answer organs, blood, or bones. The simplest answer, however, is atoms and molecules. An **atom** is the smallest constituent of a chemical element that has all the properties of an element. Atoms comprise every single piece of matter. From your sofa to the sandwich you ate yesterday, atoms in multiple combinations, or molecules, are all around us. But how is the mass of an atom expressed? In this lesson, we will learn more about atomic mass units.

## Atomic Mass Unit (AMU)

The periodic table of elements contains every atom known to mankind. Each unique atom has a unique atomic number and atomic mass. The **atomic number** is the number of protons in the atom's nucleus, while the **atomic mass** is the mass of the atom, which is the sum of the number of protons and neutrons. The atomic mass of an element is expressed in atomic mass units. **Atomic mass units** are described as a unit of measurement for atoms and molecules, just like the mass of a person may be expressed in pounds or kilograms. Hydrogen, for example, is the first element on the periodic table and has an atomic number of 1 and an atomic mass of 1.00794 amu, or atomic mass units.

## AMU Standard

According to the International Union of Pure and Applied Chemistry (IUPAC), **1 atomic mass unit** is defined as 1/12 the mass of carbon-12. Therefore, carbon-12 has a mass of 12 amu. Carbon-12 is the most abundant isotope of carbon. An **isotope** is two or more elements with the same number of protons (atomic number) but different number of neutrons. For example, carbon-12 has 6 protons, 6 electrons, and 6 neutrons and encompasses over 98% of carbon found in nature. On the other hand, carbon-13 has 6 protons, 6 electrons, and 7 neutrons; and carbon-14 has 6 protons, 6 electrons, and 8 neutrons.

Why is carbon the standard? Good question! Carbon is commonly combined with other elements; additionally, the carbon-12 isotope is highly abundant in nature. After many years of arguing, chemists and physicists agreed that carbon-12 would be the best unit of measurement for atomic masses. Previous standards included hydrogen and oxygen; however, scientists had difficulty using these elements as standards due to the distribution of their isotopes.

## Converting Units

If atoms are weighed in atomic mass units, how do we get from atomic mass units to a more common measurement like kilograms? Conversion! According to the Royal Society of Chemistry, one atomic mass unit is equal to 1.66 x 10^-27 kg. Where did this number come from? While the history of atomic masses is quite complicated, the conversion factor from atomic mass units to kilograms is related to the mole and Avogadro's constant.

The mole is a base unit that describes the amount of a substance. You can have a mole of anything: atoms, baseballs, and even carrots. According to the National Institute of Standards and Technology (NIST), the **mole** is 'the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilograms of carbon-12.' The number of atoms or molecules in one mole of substance is known as **Avogadro's constant (Na or L)**. Avogadro's constant, Na, is an experimentally defined number of 6.022 * 10 ^23 entities per mole (remember entities can be atoms, baseballs, or carrots).

Believe it or not, mathematically, moles and Avogadro's constant bring us back to atomic mass units.

An atomic mass unit is 1/12th the mass of carbon-12, therefore, the mass of carbon-12 is 12 amu. Consequently, one mole of carbon-12 has Avogadro's constant (Na) amount of atoms in 0.012 kg of carbon-12. Mathematically, this is expressed by:

(6.022 * 10^23/ mol) * 12 amu = 0.012 (kg/mol)

Dividing both sides of the equation by 12 we are left with:

(6.022 * 10^23/mol)(1 amu) = 0.001 kg/mol

Dividing both sides by Avogadro's constant, we find that 1 amu is equal to 1.66 * 10^-27 kg.

This means that atomic mass units can be easily converted to kilograms or grams. For example, carbon-12 has a mass of 12 amu. By multiplying 12 amu by 1.66 x 10^-27 kg/amu we find the mass of carbon-12 in kilograms is 1.99 * 10^-26 kg. This conversion can be used to convert atoms and molecules from atomic mass units to grams and kilograms.

## Lesson Summary

In this lesson, we have learned that the mass of atoms and molecules are expressed in atomic mass units. **Atomic mass units (amus)**, are described as 1/12 the mass of carbon-12. Therefore, carbon-12 is identified as the standard for atomic mass. Finally, the mass of atoms and molecules can be converted from atomic mass units to kilograms by the unit conversion which states:

1 amu = 1.66 * 10^-27 kg

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