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Atomic mass and isotopic mass: definition, units, and relation to mass number

Defines atomic and isotopic mass, explains units (u and SI), shows how mass number and nucleons relate, and covers isotopes, relative atomic mass and how averages differ from single-atom masses.

Author: Leandro Alegsa Creation date: November 13, 2022 Last updated: April 10, 2026

Definition

An atomic mass (often written as m_a) is the mass of a single atom of a particular chemical element. It equals the combined masses of the atom’s constituent subatomic particles: the protons, the neutrons in the nucleus, and the electrons that surround it.

Units and numerical value

While atomic mass can be expressed in everyday units such as grams, individual atoms are extremely light, so chemists and physicists normally use the unified atomic mass unit (symbol: u). By definition, 1 u equals one twelfth of the mass of a carbon-12 atom. In SI terms this is approximately 1.66053906660(50) × 10^-27 kg.

Relation to nucleons and the mass number

Because the protons and neutrons (collectively called nucleons) have masses close to 1 u each and the electrons are much lighter, a simple estimate of an atom’s atomic mass in u is the sum of its proton and neutron counts. That count is the atom’s mass number (symbol: A), which is the total number of protons plus neutrons in the nucleus. The mass number is an integer and has no units; the true atomic mass usually differs slightly from A because of nuclear binding energy and the small contribution of electron masses.

Isotopes and average atomic mass

Many elements exist naturally as mixtures of atoms with different neutron counts; each variant is an isotope. For example, the element chlorine is commonly found as two isotopes, chlorine‑35 and chlorine‑37. Both isotopes have 17 protons, but chlorine‑35 has 18 neutrons while chlorine‑37 has 20. Each isotope has its own specific atomic mass (often called the isotopic mass), roughly equal to its mass number in whole‑number u values.

The term mass number refers to the integer count of protons plus neutrons and should not be confused with atomic mass.
Relative isotopic mass is a dimensionless quantity different from isotopic mass expressed in u.
Relative atomic mass (also called atomic weight) is an average, weighted by natural isotopic abundances, and is not identical to the atomic mass of any single atom.

Historical

The first table with relative atomic masses was published by John Dalton in 1805. He obtained them on the basis of the mass ratios in chemical reactions, choosing the lightest atom, the hydrogen atom, as the "mass unit" (see Atomic mass unit) - this, however, in ignorance of the property of hydrogen as a diatomic molecule.

Further relative atomic and molecular masses were calculated for gaseous elements and compounds on the basis of Avogadro's law, i.e. by weighing and comparing known gas volumes, later also with the help of Faraday's laws. Avogadro still referred to the smallest conceivable parts as molecules. Berzelius then introduced the term atom for the smallest conceivable part of a substance. He arbitrarily set the atomic weight of oxygen equal to 100. Later researchers chose the lightest substance, hydrogen, as the standard, but set the hydrogen molecule equal to 1. For carbon they then obtained the "equivalent weight" 6, for oxygen 8.

The actual pioneer for correct atomic weights of elements was Jean Baptiste Dumas. He determined the atomic weights for 30 elements very precisely and found that 22 elements had atomic weights that were multiples of the atomic weight of hydrogen.

It was not until 1858 that Stanislao Cannizzaro introduced today's distinction between atoms and molecules. He assumed that a molecule of hydrogen consisted of two atoms of hydrogen. For the individual hydrogen atom he arbitrarily set the atomic weight 1, a hydrogen molecule consequently has a molecular mass of 2. In 1865, oxygen, whose atoms have on average approximately 16 times the mass of the hydrogen atom, was proposed as a reference element by Jean Servais Stas and assigned a mass of 16.00. The mass of the hydrogen atom is 16.00.

In 1929, W. F. Giauque and H. L. Johnston discovered that oxygen has three isotopes. This prompted IUPAP to introduce a mass scale based on m(^16O), while IUPAC continued to use _Ar(O) = 16, i.e. oxygen in its natural isotopic composition.

In 1957, A. O. Nier and A. Ölander independently proposed that _Ar(^12C) and m(^12C) = 12 u should replace the old atomic mass units. IUPAP and IUPAC then agreed on this in 1959-1961. Until that time, therefore, physicists and chemists had two slightly different mass scales. In 1960, F. Everling, L. A. König, Josef Mattauch and Aaldert Wapstra published masses of nuclides.

Until today, the carbon isotope ^12C with the mass of 12 u serves as a reference base. The atomic mass indicates how many times greater the mass of the respective atom is than 1/12 of the mass of the ^{12C atom}. As mentioned above, the atomic masses of the nuclides are approximate, but not exact, integer multiples of the mass of the hydrogen atom.

The following table shows some average (see below) relative atomic masses, i.e. atomic weights, depending on the four different reference masses:

Element	related to
Element	^natH = 1	^natO = 16	^16O = 16	^12C = 12
^natH	01,000	01,008	01,008	01,008
^natCl	35,175	35,457	35,464	35,453
^natO	15,872	16,000	16,004	15,999
^natN	13,896	14,008	14,011	14,007
^natC	11,916	12,011	12,015	12,011

Table with atomic weights in Johann Samuel Traugott Gehler's Physical Dictionary 1840

Questions and Answers

Q: What is atomic mass?

A: Atomic mass (symbol: ma) is the mass of a single atom of a chemical element. It includes the masses of the 3 subatomic particles that make up an atom: protons, neutrons and electrons.

Q: How is atomic mass expressed?

A: Atomic mass can be expressed in grams, but it is usually expressed in unified atomic mass units (unit symbol: u). 1 atomic mass unit is defined as 1/12 of the mass of a single carbon-12 atom.

Q: What does a carbon-12 atom have a mass of?

A: A carbon-12 atom has a mass of 12 u.

Q: What determines what element an atom is?

A: The number of protons an atom has determines what element it is.

Q: What are isotopes?

A: Most elements in nature consist of atoms with different numbers of neutrons. An atom of an element with a certain number of neutrons is called an isotope.

Q:What is the difference between atomic mass and its Mass Number ?

A:The atomic mass of an atom is usually within 0.1 u of the Mass Number which represents the sum total number protons and neutrons present in nucleus without any unit .

Author

AlegsaOnline.com - Atomic mass - Leandro Alegsa

Creation date: November 13, 2022
Last updated: April 10, 2026

URL: https://en.alegsaonline.com/art/7050