Atomic Number, Mass Number, and Nuclide Notation
The atomic number (Z) is the number of protons in an atom’s nucleus and identifies the element, the mass number (A) is the total number of protons and neutrons, and nuclide notation writes them with the element symbol as AZX. In brief: 3517Cl means a chlorine atom with 17 protons and 35 − 17 = 18 neutrons; two atoms with the same Z but different A are isotopes of the same element.
Nuclide notation is a compact way to describe a specific kind of atom. It is used in chemistry, nuclear physics and medicine. This article defines the terms, explains how to read and write nuclide notation, shows how to calculate the numbers of protons, neutrons and electrons, includes a table of examples and a worked set of exercises, and gives the history of the concept of atomic number.
What is the atomic number?
The atomic number, symbol Z, is the number of protons in the nucleus. It is unique for each element: hydrogen has Z = 1, carbon has Z = 6, and gold has Z = 79. In the periodic table, elements are arranged in order of increasing atomic number. In a neutral atom, the atomic number is also the number of electrons. Changing the number of protons changes the element, which happens only in nuclear reactions.
What is the mass number?
The mass number, symbol A, is the total number of nucleons (protons and neutrons) in a nucleus. It is a whole number that counts particles. The number of neutrons, N, is the difference: N = A − Z. The mass number is close to the mass of the atom in atomic mass units, but is not the same: carbon-12 has a mass of exactly 12 u by definition, while chlorine-35 has a mass of 34.969 u.
How is nuclide notation written?
A nuclide is a particular type of nucleus, defined by its numbers of protons and neutrons. In full notation, the mass number is written as a superscript on the left of the symbol and the atomic number as a subscript on the left: AZX. For example:
- 126C: carbon with 6 protons and 6 neutrons.
- 146C: carbon with 6 protons and 8 neutrons (used in radiocarbon dating).
- 23892U: uranium with 92 protons and 146 neutrons.
For an ion, the charge is written as a superscript on the right: 2713Al3+. Because the symbol already identifies the element, and so the atomic number, the subscript is often omitted: 14C or carbon-14.
Examples of nuclides
| Nuclide | Z (protons) | A | Neutrons (A − Z) | Electrons |
|---|---|---|---|---|
| 11H | 1 | 1 | 0 | 1 |
| 21H (deuterium) | 1 | 2 | 1 | 1 |
| 126C | 6 | 12 | 6 | 6 |
| 168O | 8 | 16 | 8 | 8 |
| 2311Na | 11 | 23 | 12 | 11 |
| 5626Fe | 26 | 56 | 30 | 26 |
| 23592U | 92 | 235 | 143 | 92 |
Worked examples
- Reading a nuclide. 4020Ca: Z = 20 (calcium), A = 40, neutrons = 40 − 20 = 20, electrons in the neutral atom = 20.
- Writing a nuclide. An atom has 15 protons and 16 neutrons. Z = 15 is phosphorus, and A = 15 + 16 = 31. The nuclide is 3115P.
- Missing information. A nuclide has A = 107 and 60 neutrons. Z = 107 − 60 = 47, which is silver (Ag). The nuclide is 10747Ag.
- Ions. 3216S2− has 16 protons, 16 neutrons and 16 + 2 = 18 electrons, since the charge is 2−, which means two extra electrons.
- Fraction of neutrons. In 23592U, the neutron-to-proton ratio is 143 ÷ 92 = 1.55. In 126C it is 1.00. The ratio rises for heavy nuclei, because more neutrons are needed to keep the nucleus stable.
- Balancing a nuclear equation. In the alpha decay of 22688Ra, the nucleus emits an alpha particle (42He). The sum of A and Z must be conserved: A = 226 − 4 = 222 and Z = 88 − 2 = 86. The product is 22286Rn (radon-222).
What other ways of writing a nuclide are used?
| Style | Example | Notes |
|---|---|---|
| Full nuclide notation | 146C | Shows A and Z |
| Short notation | 14C | Z is understood from the symbol |
| Name and mass number | carbon-14 | Common in text |
| Symbol and mass number with hyphen | C-14 | Common in data tables |
Who discovered the atomic number?
Mendeleev arranged the elements by atomic mass in 1869 and found that a few pairs, such as tellurium and iodine, had to be placed out of order to match their properties. In 1913, Henry Moseley measured the X-ray spectra of many elements and found that the frequencies depend on a whole number that increases by one from element to element. This number was identified as the charge on the nucleus, the atomic number. Moseley’s work showed that the atomic number, not the atomic mass, is the correct basis of the periodic law. He was killed in World War I in 1915 at the age of 27.
Which mistakes are common?
Mistake 1: Swapping the positions of A and Z
The mass number (larger) goes at the top, and the atomic number (smaller) goes at the bottom.
Mistake 2: Calculating neutrons from the atomic mass on the periodic table
Use the mass number of the specific isotope, which is a whole number.
Mistake 3: Using Z as the number of electrons in an ion
Only neutral atoms have electrons equal to Z. Ions have different numbers.
Mistake 4: Thinking that A changes in a chemical reaction
Chemical reactions do not change the nucleus. A and Z stay the same.