Define the terms proton number (atomic number) Z and nucleon number (mass number) A and be able to calculate the number of neutrons in a nucleus

5.1.2 The Nucleus

Learning Objective (Cambridge AO1 & AO2)

Students will be able to:

• Define the proton number (atomic number) \$Z\$ and the nucleon number (mass number) \$A\$.
• Read and write nuclear (nuclide) notation correctly.
• Identify isotopes of the same element.
• Calculate the number of neutrons \$N\$ in any nucleus using \$N = A - Z\$.

1. Composition of the Nucleus

• Protons (p) – charge + 1 e, mass ≈ 1 u.
• Neutrons (n) – charge 0, mass ≈ 1 u.
• Electrons orbit the nucleus; they are not counted in \$Z\$ or \$A\$.
• Protons + neutrons = nucleons.

2. Nuclear (Nuclide) Notation

A nuclide is written as

• Superscript \$A\$ (mass number) – total number of nucleons (\$A = Z + N\$).
• Subscript \$Z\$ (atomic number) – number of protons; uniquely identifies the element.
• Letter \$X\$ – chemical symbol of the element (determined solely by \$Z\$).

Example: \$^{14}_{6}\text{C}\$ = carbon nucleus with \$A = 14\$, \$Z = 6\$.

3. Key Definitions

4. Isotopes

• Isotopes are nuclides of the same element (same \$Z\$) but with different mass numbers \$A\$ (hence different \$N\$).
• They may be stable (e.g. \$^{12}{6}\text{C}\$) or radioactive (e.g. \$^{14}{6}\text{C}\$).
• In a neutral atom the number of electrons equals \$Z\$, but this does not appear in nuclear notation.

5. Relationship Between \$Z\$, \$A\$, and \$N\$

The three quantities are linked by a single linear equation:

Re‑arranged forms useful for missing‑value problems:

6. Worked Examples

1. Carbon‑12 – \$^{12}_{6}\text{C}\$

   \$N = 12 - 6 = 6\$ → 6 neutrons.

2. Calcium‑40 – \$^{40}_{20}\text{Ca}\$

   \$N = 40 - 20 = 20\$ → 20 neutrons.

3. Chlorine‑35 – \$^{35}_{17}\text{Cl}\$

   \$N = 35 - 17 = 18\$ → 18 neutrons.

4. Isotopic comparison – \$^{12}{6}\text{C}\$ vs \$^{14}{6}\text{C}\$

   \$N_{^{12}\text{C}} = 12 - 6 = 6\$

   \$N_{^{14}\text{C}} = 14 - 6 = 8\$

   The two isotopes have the same \$Z\$ (6 protons) but differ by two neutrons.

5. Finding a missing quantity – A nucleus has \$Z = 15\$ and \$A = 31\$.

   \$N = 31 - 15 = 16\$ → \$^{31}_{15}\text{P}\$ contains 16 neutrons.

7. Practice Questions

1. Calculate the number of neutrons in \$^{23}_{11}\text{Na}\$.
2. A nucleus has 92 protons and a mass number of 238. How many neutrons does it contain?
3. Identify \$Z\$ and \$A\$ for an isotope that has 20 neutrons and a total nucleon number of 40.
4. Write the nuclide notation for an isotope of iron that has 26 protons and 30 neutrons.
5. In one sentence, explain why \$^{14}{6}\text{C}\$ and \$^{12}{6}\text{C}\$ are called isotopes of the same element.
6. Given the notation \$^{209}_{83}\text{Bi}\$, state the element name, its \$Z\$, \$A\$, and \$N\$.

Answers to Practice Questions

Suggested Diagram

Common Misconceptions

• Mixing up \$Z\$ and \$A\$: \$Z\$ counts only protons; \$A\$ counts protons + neutrons.
• All isotopes have the same \$A\$: Isotopes share \$Z\$ but have different \$A\$ (and \$N\$).
• Using addition instead of subtraction: The neutron number is \$N = A - Z\$, never \$A + Z\$.
• Electrons affect \$Z\$ or \$A\$: Electron count equals \$Z\$ in a neutral atom but does not appear in nuclear symbols.
• Mass number ≈ atomic mass: \$A\$ is an integer count of nucleons; the atomic mass (in u) is a weighted average of isotopic masses.

Summary

To describe any nucleus you need two fundamental numbers:

1. \$Z\$ (atomic number) – tells you which element the nucleus belongs to.
2. \$A\$ (mass number) – tells you the total number of nucleons.

The neutron number follows directly:

Mastering these symbols lets you read nuclide notation, distinguish isotopes, and solve the majority of IGCSE/AS‑Level questions on nuclear composition.