Nucleon number and proton number

By the end of this lesson

By the end you can define proton number $Z$ and nucleon number $A$ , read both off a nuclide, and work out the number of neutrons from $A - Z$ .

Definition

Proton number (Z)

The number of protons in the nucleus. It fixes which element the atom is: every nucleus with $Z = 6$ is carbon, every nucleus with $Z = 92$ is uranium.

Definition

Nucleon number (A)

The total number of nucleons — the protons plus the neutrons — in the nucleus. Nucleons are the particles that live in the nucleus, so $A$ is sometimes called the mass number.

Two counts, one subtraction

The two numbers are easy to mix up because both count something in the nucleus, so keep the question "which particles?" in mind:

Proton number $Z$ counts protons only.
Nucleon number $A$ counts protons and neutrons together.

A nucleus therefore contains $Z$ protons and

$\text{number of neutrons} = A - Z$

neutrons. Because $A$ also counts the protons, $A$ is never smaller than $Z$ , and the two are equal only when the nucleus has no neutrons at all — which is true for ordinary hydrogen, $Z = 1$ , $A = 1$ .

nucleus	$Z$	$A$	protons	neutrons
$^{1}_{1}\text{H}$	1	1	1	0
$^{4}_{2}\text{He}$	2	4	2	2
$^{12}_{6}\text{C}$	6	12	6	6
$^{235}_{92}\text{U}$	92	235	92	143

Why nucleon number is the mass number

A proton and a neutron have almost the same mass, about $1\ \text{u}$ each, while an electron is about $1840$ times lighter and contributes almost nothing. So nearly all of an atom's mass sits in its nucleons, and counting nucleons counts the mass. That is why $A$ is called the mass number: doubling $A$ roughly doubles the mass of the atom.

Note the "roughly". The masses are not exactly $1\ \text{u}$ each, and the nucleus has a small mass defect, so $A$ is a count, not an accurate mass.

Worked example: Reading the numbers off uranium-235

A nucleus is written $^{235}_{92}\text{U}$ . State its proton number, its nucleon number and the number of neutrons it contains.

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Quick check

Multiple choiceQuestion 1 · Recall

CalculateQuestion 2 · Recall

Fill in the blanksQuestion 3 · Apply

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