Atomic Number and Mass Number

Every atom carries two whole numbers that fix its identity. The atomic number counts protons. The mass number counts protons plus neutrons together. These two integers are written beside an element's symbol. They let a chemist reconstruct the entire subatomic makeup of an atom. This includes protons, neutrons, and (for a neutral atom) electrons. No further information is needed. This bookkeeping matters because The Nuclear Atom established that mass concentrates in a tiny, positively charged nucleus. Electrons occupy the surrounding space. Atomic number and mass number describe that nucleus precisely. They are the grammar used throughout chemistry to write nuclide symbols. They also track isotopes, and later assign charges to ions. The two quantities look similar but answer different questions. Atomic number never changes for a given element. It defines which element you have. Mass number varies from atom to atom of the same element. This happens because atoms of one element can carry different numbers of neutrons. Keeping this distinction sharp is the entire content of this topic.

Key takeaways

Atomic number $Z$ = number of protons in the nucleus; it defines the element.
Mass number $A$ = number of protons + neutrons (nucleons), always a whole number.
Number of neutrons = $A - Z$ .
For a neutral atom, number of electrons = number of protons = $Z$ .
Nuclide symbol format: $^{A}_{Z}\text{X}$ , with element symbol X, mass number as left superscript, atomic number as left subscript.
Key idea: $Z$ tells you what the atom is; $A$ tells you how heavy that particular atom is.

The core insight

Atomic number ( $Z$ ) fixes identity through proton count; mass number ( $A$ ) fixes a specific atom's nucleon total. Neutrons are the flexible piece: $A - Z$ gives how many are present, and this difference is what later distinguishes isotopes of the same element.

The physical picture

An atom's nucleus is built from two kinds of nucleons: protons, which carry a positive charge of $+1$ (in units of elementary charge $e$ ), and neutrons, which carry no charge. The number of protons is sacred — change it, and you have transmuted the atom into a different element entirely. The number of neutrons, by contrast, can vary somewhat for a given element without changing what element it is; atoms of the same element with different neutron counts are called isotopes, a topic developed fully in Isotopes and Atomic Symbols. Chemists give two names to these two nucleon counts. The atomic number, symbol $Z$ , is the number of protons. The mass number, symbol $A$ , is the total number of protons and neutrons combined — the total nucleon count. Because electrons are roughly 1836 times lighter than a proton or neutron, they contribute negligibly to an atom's mass, so $A$ is effectively the whole number of nucleons that make up nearly all the atom's mass. For a neutral atom, the number of electrons orbiting the nucleus must exactly equal the number of protons, so that the total charge is zero. This gives a clean, memorizable chain: $Z$ protons, $Z$ electrons (if neutral), and $A - Z$ neutrons.

Figure

Anatomy of a nuclide: sodium-23, with Z = 11 and A = 23

The core relations

Z = \text{number of protons}

where: $Z$ is the atomic number; it is fixed for every atom of a given element and equals that element's position identifier on the periodic table.

A = Z + N

where: $A$ is the mass number (total nucleons), $Z$ is the atomic number (protons), and $N$ is the number of neutrons.

N = A - Z

where: this rearrangement is the everyday tool for finding neutron count once $A$ and $Z$ are known.

\text{electrons (neutral atom)} = Z

where: charge neutrality requires the count of negatively charged electrons to equal the count of positively charged protons.

{}^{A}_{Z}\text{X}

where: X is the one- or two-letter element symbol, $A$ is written as a left superscript, and $Z$ is written as a left subscript, both placed before the symbol.

Derivation AFrom nucleon counting to the nuclide symbol

Goal. Show how the definitions of $Z$ and $A$ combine into a single consistent labeling system, and confirm that the labeling contains no redundant or contradictory information.

Step 1. Start from the two independent countable quantities. A nucleus is fully specified, for the purposes of general chemistry, by two independent counts: how many protons it holds and how many neutrons it holds. Call these $Z$ and $N$ . Both are non-negative integers.

Step 2. Define the mass number as their sum. Because protons and neutrons have nearly identical mass (each close to 1 atomic mass unit) and electrons contribute negligibly, the total mass of the nucleus in whole-number units is captured by

A = Z + N .

This single equation is a definition, not a measured law — $A$ is defined to be the sum, so it carries no new physical information beyond $Z$ and $N$ individually. It is, however, more convenient because $A$ is what shows up directly in an atom's approximate atomic mass.

Step 3. Show $Z$ and $A$ together are sufficient to recover everything. Given $Z$ and $A$ for any atom, neutron count follows immediately:

N = A - Z .

Given $Z$ alone, the identity of the element is fixed, because the periodic table orders elements by atomic number. Given that the atom is neutral, the electron count is fixed too:

e^{-} = Z .

Hence the pair $(Z, A)$ is a complete, non-redundant description of a neutral atom's subatomic composition — three quantities (protons, neutrons, electrons) are recoverable from just two numbers, because charge neutrality supplies the third relation for free.

Step 4. Assemble the nuclide symbol. Chemists write this pair directly on the element symbol as

{}^{A}_{Z}\text{X} .

Because the atomic number is already implied by the symbol X (every element has one and only one $Z$ ), the subscript $Z$ is sometimes dropped in casual writing — e.g., $^{23}\text{Na}$ instead of $^{23}_{11}\text{Na}$ — but including it explicitly is good practice and is required in this treatment.

Step 5. Sanity check with a limiting case. Consider the limiting case $N = 0$ , meaning a nucleus with no neutrons at all. Then $A = Z + 0 = Z$ , so mass number equals atomic number exactly. This is realized physically only for ordinary hydrogen-1 (protium), where $Z = 1$ and $A = 1$ , confirming the formula behaves sensibly at its simplest possible input.

Worked examples

Example 1 — Aluminum-27. An aluminum atom is represented as $^{27}_{13}\text{Al}$ . Aluminum's atomic number is fixed at $Z = 13$ (this is why the element is aluminum at all), and the mass number given is $A = 27$ . Protons:

Z = 13

Neutrons:

N = A - Z = 27 - 13 = 14

Electrons (neutral atom):

e^{-} = Z = 13

So a neutral aluminum-27 atom contains 13 protons, 14 neutrons, and 13 electrons. Notice the asymmetry deliberately: protons and neutrons are not equal here (13 versus 14), which confirms the calculation is not silently relying on some hidden assumption that $N = Z$ .

Example 2 — An unknown nuclide with 38 protons and 50 neutrons. Suppose a nucleus is reported to contain 38 protons and 50 neutrons, and you are asked to write its full nuclide symbol and state its mass number. Atomic number:

Z = 38

Checking a periodic table, $Z = 38$ corresponds to strontium, symbol Sr. Mass number:

A = Z + N = 38 + 50 = 88

Nuclide symbol:

{}^{88}_{38}\text{Sr}

Electron count, assuming the atom is neutral:

e^{-} = Z = 38

This example deliberately uses non-round, unequal numbers (38 protons, 50 neutrons — a gap of 12, not a clean multiple) to show the addition $A = Z + N$ must be carried out explicitly rather than guessed from a pattern.

Limiting cases & common traps

Situation	What happens	Why
$N = 0$	$A = Z$	No neutrons means mass number collapses to atomic number (only true for protium, $^1_1\text{H}$ )
Very large $Z$ (heavy elements)	$N$ typically exceeds $Z$ substantially	Nuclear stability requires extra neutrons to offset proton-proton repulsion in large nuclei
Atom is an ion, not neutral	$e^{-} \neq Z$	Electron count only equals $Z$ for neutral atoms; charged species are covered under Ions and Ionic Charge
Same element, different $A$	$Z$ identical, $N$ differs	This defines isotopes, not different elements

The chemist behind it

The modern notions of atomic number and mass number emerged from early twentieth-century nuclear physics, but it was the chemist and physicist Henry Moseley who gave atomic number its central meaning. Before Moseley's work, elements were ordered on the periodic table largely by increasing atomic mass, which produced awkward inconsistencies — some elements seemed out of order when arranged strictly by mass. Moseley measured the X-ray spectra emitted by various elements and found a precise mathematical relationship between X-ray frequency and a small integer characteristic of each element. That integer, he showed, was the true organizing principle of the periodic table: the number of positive charges — protons — in the nucleus. This let chemists finally order the periodic table correctly, by atomic number rather than atomic mass, resolving several long-standing anomalies (such as the placement of tellurium before iodine).

Origins · 1 minHenry Gwyn Jeffreys Moseley and how this was discovered

Henry Gwyn Jeffreys Moseley

1887–1915 · Early twentieth-century England, working in the wake of Rutherford's nuclear model

Moseley's law connected characteristic X-ray frequencies of elements to a small whole number he identified as nuclear charge, giving atomic number its physical meaning as a proton count rather than an arbitrary ordering label. His experimental program placed the periodic table on a firm quantitative foundation, though his career and life were cut short at age 27 during the First World War.

Ask the tutor: If two nuclides have the same mass number but different atomic numbers, what are they called and how do their neutron counts compare?

Can two atoms have the same atomic number but different mass numbers?

Yes. This is precisely the definition of isotopes — atoms of the same element (same $Z$ , same number of protons) that differ in neutron count and therefore in mass number $A$ . Carbon-12 and carbon-14 both have $Z = 6$ but different $A$ (12 and 14). The full treatment of this idea belongs to Isotopes and Atomic Symbols.

Does mass number equal the atomic mass listed on the periodic table?

No. Mass number $A$ is always a whole number — a simple count of protons plus neutrons in one specific atom. The atomic mass on the periodic table is a weighted average over all naturally occurring isotopes of that element, so it is usually not an integer (chlorine's atomic mass, for instance, is about 35.45, reflecting a mixture of chlorine-35 and chlorine-37 nuclei).

What happens to electron count if the atom is not neutral?

For a neutral atom, electrons equal protons, so $e^{-} = Z$ . If the atom has gained or lost electrons to become an ion, that equality breaks: a cation has fewer electrons than $Z$ , an anion has more. This relationship is developed fully in Ions and Ionic Charge, but the atomic number itself is unaffected by ionization — losing or gaining electrons never changes which element the atom is.

Why does mass number use protons plus neutrons rather than including electron mass?

Electrons are about 1836 times less massive than a proton or neutron, so their contribution to total atomic mass is negligible at the level of whole-number bookkeeping. Defining $A$ purely from nucleon count keeps it an exact integer tied directly to nuclear structure, which is what makes it useful for writing nuclide symbols and reasoning about The Nuclear Atom.