Atomic Mass
Atomic mass is the weighted average mass of all naturally occurring isotopes of an element, expressed in atomic mass units (u or amu), where 1 u is defined as one-twelfth the mass of a carbon-12 atom. Because most elements exist as mixtures of isotopes with different natural abundances, the atomic mass reported on the periodic table is not a whole number. Atomic mass is essential for converting between grams and moles of a substance using the molar mass concept.
Key Formula
Atomic Mass = Σ (mass of isotope i × fractional abundance of isotope i)
LaTeX: M = \sum_{i} (m_i \times a_i)
| Symbol | Meaning | Unit |
|---|---|---|
| M | Average atomic mass | u (amu) |
| m_i | Mass of isotope i | u (amu) |
| a_i | Fractional (decimal) natural abundance of isotope i | dimensionless |
Worked Example
Problem
Calculate the average atomic mass of chlorine. Cl-35 has mass 34.969 u and abundance 75.77%; Cl-37 has mass 36.966 u and abundance 24.23%.
Solution
Step 1 — Convert percentages to decimals: Cl-35: 75.77% → 0.7577 Cl-37: 24.23% → 0.2423 Step 2 — Multiply each isotope mass by its fractional abundance: Cl-35: 34.969 × 0.7577 = 26.496 u Cl-37: 36.966 × 0.2423 = 8.957 u Step 3 — Sum the contributions: M = 26.496 + 8.957 = 35.453 u
Answer
Average atomic mass of chlorine ≈ 35.45 u (matches the periodic table value).
Isotopes of Chlorine and Their Contributions to Average Atomic Mass
| Isotope | Mass (u) | Natural Abundance (%) | Contribution (u) | Protons / Neutrons |
|---|---|---|---|---|
| Cl-35 | 34.969 | 75.77 | 26.496 | 17 / 18 |
| Cl-37 | 36.966 | 24.23 | 8.957 | 17 / 20 |
| Weighted Average | — | 100.00 | 35.453 | — |
Interactive Tools
NIST Atomic Weights and Isotopic Compositions
Official database of isotopic masses and natural abundances for all elements.
Open Tool
Wikimedia Commons, CC BY-SA
Related Terms
Nuclear Symbol
A nuclear symbol (also called nuclide symbol) is a compact notation used to represent a specific isotope of an element, showing the element symbol with its mass number (A) as a superscript and atomic number (Z) as a subscript on the left. The mass number A equals the sum of protons and neutrons in the nucleus, while Z equals the number of protons (which defines the element). Nuclear symbols allow chemists and physicists to unambiguously specify isotopes in nuclear equations, radioactive decay series, and isotope chemistry.
Atomic Radius
Atomic radius is a measure of the size of an atom, typically defined as half the distance between the nuclei of two identical adjacent atoms in a covalent bond (covalent radius) or in a metallic lattice (metallic radius). Atomic radius decreases across a period (left to right) because increasing nuclear charge pulls electrons closer to the nucleus, while it increases down a group because additional electron shells increase the average distance of the outermost electrons from the nucleus. These periodic trends directly influence bond lengths, ionic sizes, and many physical properties.
Effective Nuclear Charge
Effective nuclear charge (Z_eff) is the net positive charge experienced by a valence electron after accounting for the shielding (screening) effect of inner electrons, which partially cancel the attraction from the nucleus. It is calculated as Z_eff = Z − S, where Z is the actual atomic number and S is the shielding constant. Effective nuclear charge increases across a period because additional protons are added while shielding remains approximately constant, explaining trends in atomic radius, ionization energy, and electron affinity.
From Greek "atomos" (indivisible) and Latin "massa" (lump or mass). The concept of comparing atomic masses dates to John Dalton's atomic theory (1803) and was refined with the discovery of isotopes by Frederick Soddy in 1913.