Define the terms proton number (atomic number) \$Z\$ and nucleon number (mass number) \$A\$, and be able to calculate the number of neutrons \$N\$ in a nucleus.
Key Definitions
Proton number (Atomic number) \$Z\$: The number of protons in the nucleus of an atom. It determines the element’s identity.
Nucleon number (Mass number) \$A\$: The total number of nucleons (protons + neutrons) in the nucleus.
Neutron number \$N\$: The number of neutrons in the nucleus. It can be found from \$N = A - Z\$.
Relationship Between \$Z\$, \$A\$, and \$N\$
The three quantities are related by the simple equation:
\$N = A - Z\$
Re‑arranging gives:
\$A = Z + N\$
Calculating Neutrons – Worked Examples
Find the number of neutrons in a carbon‑12 atom (\$^{12}_{6}\text{C}\$).
Given: \$A = 12\$, \$Z = 6\$.
Using \$N = A - Z\$:
\$N = 12 - 6 = 6\$
Carbon‑12 has 6 neutrons.
Determine \$N\$ for an isotope written as \$^{40}_{20}\text{Ca}\$.
Given: \$A = 40\$, \$Z = 20\$.
\$N = 40 - 20 = 20\$
Calcium‑40 contains 20 neutrons.
What is the neutron number for an unknown isotope of chlorine that has \$Z = 17\$ and \$A = 35\$?
\$N = 35 - 17 = 18\$
Thus \$^{35}_{17}\text{Cl}\$ has 18 neutrons.
Practice Questions
Calculate the number of neutrons in \$^{23}_{11}\text{Na}\$.
A nucleus has 92 protons and a mass number of 238. How many neutrons does it contain?
Identify \$Z\$ and \$A\$ for an isotope that has 20 neutrons and a total nucleon number of 40.
Answers to Practice Questions
Question
Solution
1
\$N = 23 - 11 = 12\$ neutrons.
2
\$N = 238 - 92 = 146\$ neutrons.
3
Given \$N = 20\$ and \$A = 40\$, \$Z = A - N = 40 - 20 = 20\$. So \$Z = 20\$, \$A = 40\$ (i.e., \$^{40}_{20}\text{Ca}\$).
Suggested diagram: A schematic of a nucleus showing protons (positive signs) and neutrons (neutral symbols) with labels for \$Z\$, \$N\$, and \$A\$.
Common Misconceptions
Confusing \$Z\$ with \$A\$: \$Z\$ counts only protons, whereas \$A\$ counts both protons and neutrons.
Assuming all isotopes of an element have the same \$A\$: Different isotopes have the same \$Z\$ but different \$A\$ (and thus different \$N\$).
Neglecting the minus sign in \$N = A - Z\$: Remember to subtract, not add.
Summary
To identify a nucleus you need two numbers:
\$Z\$ – tells you the element.
\$A\$ – tells you the total number of nucleons.
The neutron number is simply the difference between them, \$N = A - Z\$. Mastery of these concepts allows you to interpret nuclear notation and solve a wide range of IGCSE physics problems.