Atomic Mass, Subatomic Particles, and Relative Atomic Mass

Chemistry is the scientific discipline dedicated to understanding physical phenomena at an extraordinarily small scale, specifically the atomic and subatomic scales.
Understanding atomic and subatomic structures provides the foundation for comprehending the universe, predicting chemical reactions, and synthesizing useful materials for human application.
Measuring matter at the atomic scale requires specialized mass units rather than macro-scale units like kilograms or grams.
Historically, the chemistry community used the atomic mass unit, abbreviated as $\text{AMU}$ .
The modern, standardized unit is the unified atomic mass unit, denoted simply by the symbol $\text{u}$ .
The precise conversion definition of a unified atomic mass unit to kilograms is: $1\,\text{u} = 1.660540 \times 10^{-27}\,\text{kg}$
In decimal notation, $1.660540 \times 10^{-27}\,\text{kg}$ is written as $0.$ followed by $26$ zeros and the sequence $1660540$ : $0.000000000000000000000000001660540\,\text{kg}$
The numerical value of the unified atomic mass unit was chosen so that individual atoms, protons, and neutrons would have clean, approximately integer mass values.

Atoms consist of three primary subatomic particles: protons, neutrons, and electrons.
Proton Mass:
- Roughly equal to $1\,\text{u}$ .
- More precisely, a proton has a mass of approximately $1.007\,\text{u}$ .
Neutron Mass:
- Roughly equal to $1\,\text{u}$ .
- More precisely, a neutron has a mass of approximately $1.008\,\text{u}$ , making it slightly heavier than a proton.
Electron Mass:
- An electron has a mass far smaller than that of a proton or a neutron.
- An electron's mass is approximately $\frac{1}{2000}$ (one two-thousandth) of the mass of a single proton or neutron.
Nuclear Mass Concentration:
- Because electrons contribute a negligible fraction to the total mass of an atom, virtually all atomic mass is concentrated in the nucleus.
- An atom's overall atomic mass is primarily determined by the combined quantity of protons and neutrons in its nucleus.

An element is defined exclusively by its atomic number, which is the total number of protons located in the nucleus of its atoms.
The atomic number is displayed at the top of each element's entry on the periodic table of elements.
Examples of element identities defined by proton count:
- Hydrogen ( $\text{H}$ ): Atomic number $1$ (contains exactly $1$ proton in its nucleus by definition).
- Calcium ( $\text{Ca}$ ): Atomic number $20$ (contains exactly $20$ protons in its nucleus by definition).
- Krypton ( $\text{Kr}$ ): Atomic number $36$ (contains exactly $36$ protons in its nucleus by definition).

Isotopes are defined as different variants of a given chemical element that share the same atomic number (same number of protons) but possess different numbers of neutrons.
Hydrogen Isotopes:
- The most abundant isotope of hydrogen in the universe contains $1$ proton, $0$ neutrons, and $1$ electron (in a neutral state).
- Approximately $99.98\%$ of all hydrogen present in the universe consists of this zero-neutron isotope.
- Other isotopes of hydrogen exist containing $1$ or $2$ neutrons.
Mass of Hydrogen:
- The total mass of the zero-neutron hydrogen atom equals the combined mass of $1$ proton and $1$ electron.
- Because the electron's mass is nearly negligible compared to the proton, the mass of this hydrogen atom is roughly $1\,\text{u}$ .
- Calculating the precise combined mass of $1$ proton and $1$ electron yields approximately $1.008\,\text{u}$ .

Average Atomic Mass Definition: The value listed at the bottom of an element's entry on the periodic table represents the weighted average mass of all naturally occurring isotopes of that element.
Weighted Average Calculation Mechanics:
- The average atomic mass is calculated by multiplying the atomic mass of each isotope by its fractional natural abundance and summing the results.
- Example Calculation: Consider a hypothetical element with two naturally occurring isotopes:
- Isotope 1 has an abundance of $80\%$ ( $0.80$ ) and an atomic mass of $5\,\text{u}$ .
- Isotope 2 makes up the remaining $20\%$ ( $0.20$ ) of the element and has an atomic mass of $6\,\text{u}$ .
- The weighted average atomic mass is calculated as: $(0.80 \times 5\,\text{u}) + (0.20 \times 6\,\text{u}) = 4.0\,\text{u} + 1.2\,\text{u} = 5.2\,\text{u}$
Terminology Distinctions:
- Older chemistry texts and traditional nomenclature frequently refer to average atomic mass as atomic weight.
- The term "atomic weight" is technically incorrect because it refers to mass rather than gravitational force/weight. The accurate terminology is average atomic mass.

Periodic tables often express values without explicitly appending the unit symbol $\text{u}$ , making these quantities dimensionless numbers.
Dimensionless atomic mass values are referred to as relative atomic mass.
Relative atomic mass compares the average mass of an atom of a given element to a relative standard scale:
- Carbon: Has a relative atomic mass of roughly $12$ , signifying that an average carbon atom is approximately $12$ times heavier than an average hydrogen atom.
- Oxygen: Has a relative atomic mass of $16$ , which corresponds directly to an average atomic mass of $16\,\text{u}$ when units are attached.