What is an isotope: atoms of the same element that share the same atomic number \(Z\) (same number of protons) but have different numbers of neutrons, producing different mass numbers \(A\).
Atomic number, neutron number, and mass number
For any atom (or nuclide), the defining counts are:
- Atomic number \(Z\): number of protons in the nucleus (element identity).
- Neutron number \(N\): number of neutrons in the nucleus (isotope identity within an element).
- Mass number \(A\): total number of nucleons, \(A = Z + N\).
Isotopes share \(Z\) and differ in \(N\), so they differ in \(A\). Electrons do not affect isotope identity; changing electron count produces ions, not new isotopes.
Nuclide (isotope) notation
A compact notation writes the mass number as a left superscript and atomic number as a left subscript:
\[ {}^{A}_{Z}\mathrm{X}, \]where \(\mathrm{X}\) is the element symbol. The neutron number is implied by \(N = A - Z\).
The word “nuclide” refers to a specific nuclear composition \((Z, N)\). “Isotope” is used when comparing nuclides of the same element (same \(Z\)) that differ in \(N\).
Example set: carbon isotopes
Carbon has \(Z = 6\). Common isotopes differ by neutron count:
| Isotope | \(Z\) (protons) | \(N\) (neutrons) | \(A\) (mass number) | Stability note |
|---|---|---|---|---|
| \({}^{12}_{6}\mathrm{C}\) | 6 | 6 | 12 | Stable (most abundant) |
| \({}^{13}_{6}\mathrm{C}\) | 6 | 7 | 13 | Stable (minor abundance) |
| \({}^{14}_{6}\mathrm{C}\) | 6 | 8 | 14 | Radioisotope (decays) |
Isotopes and average atomic mass
The atomic mass shown on the periodic table is usually a weighted average of the isotopic masses based on natural abundance. If an element has isotopes \(i\) with isotopic mass \(m_i\) and fractional abundance \(f_i\) (with \(\sum f_i = 1\)), then the average atomic mass is
\[ \overline{m} = \sum_i f_i m_i. \]This weighted-average idea explains why periodic-table atomic masses are rarely integers, even though individual isotopes have integer mass numbers \(A\).
Mass number versus isotopic mass
The mass number \(A\) is a count of protons and neutrons, not the measured mass in atomic mass units. The isotopic mass of a nuclide deviates slightly from \(A\) because of nuclear binding energy and the reference scale that defines \(1\ \text{u}\) using \({}^{12}\mathrm{C}\).
Visualization: isotopes as changes in neutron count
Common misconceptions
- Isotopes versus ions: isotopes differ in neutrons; ions differ in electrons.
- Mass number versus atomic mass: \(A\) is an integer count; periodic-table atomic mass is a weighted average and is usually non-integer.
- Chemical behavior: isotopes have nearly the same chemistry because they share the same electron configuration; measurable differences arise mainly through mass-dependent effects (isotope effects).