Know the relationship between the proton number and the relative charge on a nucleus

5.1.2 The Nucleus

Objective

To understand how the proton number (atomic number Z) determines the relative electric charge of a nucleus, and to become familiar with the nuclear terminology required by the Cambridge IGCSE 0625 syllabus.

1. Quick‑Reference Table

2. Structure of the Nucleus

• The nucleus is the tiny, dense centre of an atom.
• It contains two kinds of nucleons:
  • Protons – each carries a charge of +1 e ( +1.602 × 10⁻¹⁹ C).
  • Neutrons – electrically neutral (0 e).
• The number of protons = atomic number Z. Changing Z gives a different element.
• The total number of nucleons = mass number A.
  Relationship: A = Z + N, where N is the neutron number.

3. Nuclide Notation

A nuclide is written as _Z^A X, where X is the chemical symbol.

4. Isotopes

• Atoms of the same element (same Z) that have different mass numbers (different A) are called isotopes.
• Example: ¹²₆C (N = 6) and ¹⁴₆C (N = 8) are isotopes of carbon.

5. Relationship Between Proton Number and Nuclear Charge

The elementary charge carried by a single proton is

e = 1.602 × 10⁻¹⁹ C

For a nucleus containing Z protons, the **relative nuclear charge** is

Q = +Z e

Thus the nuclear charge is directly proportional to the proton number. A neutral atom contains exactly Z electrons, giving an overall charge of zero.

6. Worked Examples

7. Implications for Chemical Behaviour

1. The nuclear charge (Z) defines the element’s identity; changing Z gives a different element.
2. A neutral atom has Z electrons, balancing the +Z e nuclear charge.
3. Ions form when the number of electrons differs from Z.
   Net charge = (Z − Nₑ) e, where Nₑ is the number of electrons.

8. Nuclear Reactions (Extension)

• Fission – a heavy nucleus splits into two (or more) lighter nuclei, releasing neutrons and energy.
  Example: ^²³⁸U → ^²³⁶U + ^⁴He (α‑particle) + 2 n + energy.
  Numerical illustration: The average energy released in the fission of one ^²³⁸U nucleus is ≈ 200 MeV ≈ 3.2 × 10⁻¹¹ J. For 1 g of ^²³⁸U (≈ 2.55 × 10²¹ nuclei) this corresponds to ≈ 8 × 10¹⁰ J, an order‑of‑magnitude of 10¹¹ J (about the energy released by 2 t of TNT).
• Fusion – two light nuclei combine to form a heavier nucleus, also releasing energy.
  Example: ^²H + ^³H → ^⁴He + n + 17.6 MeV.

9. Experimental Evidence – Rutherford Scattering

• 1911 experiment: α‑particles from a radioactive source were directed at a thin gold foil.
• Most particles passed straight through, but a small fraction were deflected at large angles.
• This could only be explained if the positive charge and most of the atomic mass were concentrated in a tiny central nucleus.

10. Radioactivity – Detection and Background Radiation

Although not required for detailed calculations, the syllabus expects a basic understanding of radiation detection and background levels.

• Background radiation sources:
  • Cosmic rays from space.
  • Radon gas released from rocks and soil.
  • Terrestrial radionuclides (e.g., uranium, thorium) in building materials.
• Geiger‑Müller (GM) counter:
  • Detects ionising radiation by counting individual events.
  • Readout is given in counts per second (cps) or counts per minute (cpm).

Suggested Classroom Activity

1. Place a GM counter in the centre of the classroom and record the count rate for 2 minutes – this is the background count.
2. Bring a small sealed source of a known β‑emitter (e.g., ^⁹⁰Sr) and record the count rate at 5 cm distance for another 2 minutes.
3. Subtract the background count from the source count to obtain the net activity of the source.
4. Discuss why the background count is never zero and how shielding (e.g., a sheet of lead) reduces the measured rate.

11. Common Misconceptions

• Neutrons contribute to nuclear charge.
  Clarification: Neutrons are neutral; only protons determine the nuclear charge.
• All atoms of an element have the same net charge.
  Clarification: Atoms of the same element have the same Z, but they may be neutral or exist as positively/negatively charged ions.
• “Mass number” and “atomic number” are interchangeable.
  Clarification: A = Z + N counts all nucleons; Z counts only protons.

12. Suggested Diagram

Summary

The relative charge of a nucleus is given by the simple linear relationship Q = +Z e. This charge, together with the mass number A = Z + N, uniquely identifies a nuclide, explains isotopic variation, and underpins the formation of ions and the overall electrical neutrality of atoms. Mastery of these ideas provides the foundation for understanding nuclear reactions, the experimental evidence for the nuclear model, and basic radiation detection techniques required in the Cambridge IGCSE 0625 syllabus.