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# atomic mass unit (AMU or amu)

## What is atomic mass unit (AMU or amu)?

The atomic mass unit (AMU or amu) of an element is a measure of its atomic mass. Also known as the dalton (Da) or unified atomic mass unit (u), the AMU expresses both atomic masses and molecular masses.

AMU is defined as one-twelfth the mass of an atom of carbon-12 (12C). 12C is the most abundant natural carbon isotope, accounting for over 98% of carbon found in nature. It has an AMU of 12.

## Atomic mass and atomic mass unit

Each element in the periodic table consists of atoms, and each atom has a unique atomic mass and unique atomic number. The atomic number refers to the number of protons in the atom's nucleus, while atomic mass reflects the sum of the number of protons and neutrons. It is expressed in AMU or Da.

One AMU is the average of the proton rest mass and the neutron rest mass. This can be expressed as the following:

1 AMU = 1.67377 x 10-27 kilograms = 1.67377 x 10-24 grams

Carbon-12 is considered a reference for all atomic mass calculations. Thus, the mass of any isotope of any element is expressed in terms of the 12C standard of AMU.

### Examples

• The mass of one atom of helium-4 = 4.0026 AMU
• The mass of one atom of sulfur-32 = 31.972 AMU
• The mass of one atom of hydrogen-1 = 1.007 AMU
• The mass of one atom of titin (the largest known protein) = 3 x 106 AMU

Each 12C atom has six protons and six neutrons in its nucleus, adding up to an atomic mass of 12 AMU. Electrons have a low mass, so they are assumed to have a negligible effect. Consequently, the nucleus accounts for almost the entire mass of the atom of any element, which means that a single proton or neutron has an approximate mass of 1 AMU.

Nonetheless, the term approximate matters because the masses of individual atoms in elements -- other than carbon -- are not whole numbers (see above examples). This is because mass is affected by the interactions of various particles in the nucleus. And, even though the mass of electrons is small, it is taken into account when calculating the mass of one atom.

## History of atomic mass unit

In 1803, John Dalton suggested a way to express relative atomic mass in terms of hydrogen-1 (protium). Subsequently, Wilhelm Ostwald suggested expressing the relative atomic mass as one-sixteenth the mass of oxygen. But, when isotopes and isotopic oxygen were discovered, it created confusion about how to express the relative atomic mass of other elements. Consequently, the definition of AMU diverged with some scientists expressing it based on natural oxygen, while others based it on the oxygen-16 isotope. The latter remained a popular way to express AMU until 1961.

That year, a way to eliminate the confusion was found. It was suggested that carbon-12 be used as the basis of expressing AMU instead of oxygen or oxygen-16. The new unit was given the symbol u and Da. However, the symbol AMU didn't disappear, and scientists continued to use it even after the shift to carbon-12.

Today, all three symbols are used to express atomic mass unit: AMU, u and Da:

1 AMU = 1 u = 1 Da

## Unified atomic mass unit

The unified atomic mass unit -- expressed as lowercase u -- is generally considered a synonym for AMU. It is a physical constant accepted for use in the International System of Units (SI) measurement system. Although the phrase AMU is more commonly used today, it refers to unified AMU.

The relationship between the unified AMU and the SI unit for mass (kg), is expressed by Avogadro's number NA. By the definition of NA, the mass of a 12C atom at rest and in its ground state is 12 grams or 0.012 kg.

1 AMU = 1.6605 x 10-27 kg

## Differentiating isotopes with atomic mass unit

The AMU is a useful way to differentiate between isotopes by expressing their relative masses. An isotope refers to multiple elements with the same atomic number -- number of protons -- but a different atomic mass due to a different number of neutrons.

### Example 1

An atom of uranium-235 (U-235) has an AMU of approximately 235.

However, an atom of uranium-238 (U-238) is slightly more massive and thus has a larger mass. Its AMU is 238.

The AMU difference occurs because U-238, which is the most abundant naturally occurring uranium isotope, has three more neutrons in its atom than U-235. U-235 is used in nuclear reactors to generate nuclear energy by the process of nuclear fission. It is also one of the key ingredients of atomic bombs.

### Example 2

 Isotope Number of electrons Number of protons Number of neutrons AMU (protons + neutrons) Carbon-12 6 6 6 12 Carbon-13 6 6 7 13 Carbon-14 6 6 8 14

## What is atomic weight?

Atomic weight, or relative atomic mass, is the ratio of the average mass of an element's atoms to some standard. Although the terms atomic weight and atomic mass are used interchangeably, they have different meanings. Atomic weight implies a force exerted in a gravitational field, while mass doesn't. Specifically, the atomic weight of an element is the weighted average of the atomic masses of its different isotopes.

### Example

Carbon is a mixture of two isotopes: 12C and 13C.

AMU of 12C = 12

AMU of 13C = 13

Availability of 12C = 98.89%

Availability of 13C = 1.11%

Average AMU of 12C and 13C = ((98.89 / 100) x 12) + ((1.11 / 100) x 13) = 12.011 AMU

Atomic weight of carbon = 12.011 AMU

This example shows how the atomic weight of an element differs from the atomic masses of its isotopes. That's why atomic weight is not the same as atomic mass. Rather, it is more accurate to call it relative atomic mass.

Atomic weight is a fundamental concept in chemistry. Most chemical reactions are affected by the numerical relationships between atoms. However, when chemists need to measure reactants and products, they do not count individual atoms. Rather, they calculate atomic weights to guide their decisions.

See our table of physical units.

This was last updated in July 2022

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