Describe the composition of the nucleus in terms of protons and neutrons

5.1.2 The Nucleus

Objective

Describe the composition of the nucleus in terms of protons and neutrons, use the symbols Z, A, N correctly, and write nuclear (nuclide) notation.

1. What the Nucleus Is

• The nucleus is the tiny, dense centre of an atom.
• It contains two kinds of nucleons:
  • Protons (p) – positively charged, mass ≈ 1 u.
  • Neutrons (n) – electrically neutral, mass ≈ 1 u.
• Electrons orbit the nucleus; their mass (≈ 0.0005 u) is negligible compared with the nucleons.

2. Charges and Masses of Sub‑Atomic Particles

3. Atomic Number, Mass Number and Neutron Number

• Z – atomic number: number of protons in the nucleus. It also determines the element’s chemical symbol (e.g., Z=6 → carbon).
• A – mass number: total number of nucleons (protons + neutrons). A is approximately the mass of the nucleus in atomic mass units.
• N – neutron number: N = A – Z.

Because each proton carries a charge of +1 e, the total nuclear charge is +Z e.

4. Nuclide (Nuclear) Notation

• Write the mass number as a superscript, the atomic number as a subscript, then the element symbol:

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

• Example: ⁴₂He for a helium‑4 nucleus.

5. Worked Example – Number of Neutrons

6. Isotopes – Same Z, Different A

Atoms of the same element have the same atomic number but may contain different numbers of neutrons. These variants are called isotopes.

Both isotopes are carbon because they have Z=6, but they differ in mass and nuclear stability.

7. Stability, Binding Energy (brief)

• Protons repel each other electrically (Coulomb repulsion).
• The strong nuclear force, acting over very short distances, binds protons and neutrons together.
• The balance between these forces determines whether a nucleus is stable.
• Conceptual link to energy: the mass defect Δm = ( Z m_p + N m_n ) – m_nucleus corresponds to the binding energy E = Δm c². (No calculation required at this level.)

8. Link to Nuclear Reactions (Supplement)

Understanding nuclear composition is essential for describing fission and fusion.

8.1 Fission – heavy nucleus splits

Typical example (no numerical masses required):

$$^{235}_{92}\text{U} + ^{1}_{0}\text{n} \;\longrightarrow\; ^{141}_{56}\text{Ba} + ^{92}_{36}\text{Kr} + 3\,^{1}_{0}\text{n}$$

• Initial nucleus: Z=92, A=235.
• Products have a total Z of 56 + 36 = 92 and a total A of 141 + 92 + 3 = 236, the same as the reactants (235 + 1).
• The combined mass of the products is slightly less than the mass of the reactants; the missing mass is released as energy (E = Δm c²).

8.2 Fusion – light nuclei combine

Typical example (again, no detailed mass numbers required):

$$^{2}_{1}\text{H} + ^{3}_{1}\text{H} \;\longrightarrow\; ^{4}_{2}\text{He} + ^{1}_{0}\text{n}$$

• Reactants: total Z=1 + 1 = 2, total A=2 + 3 = 5.
• Products: Z=2 + 0 = 2, A=4 + 1 = 5 – the same numbers are conserved.
• The mass of the helium nucleus plus the neutron is slightly less than the mass of the two hydrogen isotopes; the mass defect appears as released energy.

9. Suggested Diagram

Summary

• The nucleus consists of protons and neutrons (nucleons).
• Z = number of protons → determines the element.
• A = total nucleons; N = A – Z = number of neutrons.
• Nuclide notation: ^A_Z X (mass number as superscript, atomic number as subscript, then element symbol).
• Isotopes have the same Z but different A (e.g., ¹²₆C and ¹⁴₆C).
• Stability results from the strong nuclear force overcoming electrostatic repulsion; the binding energy is given by E = Δm c².
• These ideas underpin nuclear reactions such as fission and fusion, where the total Z and A are conserved but a small mass defect is released as energy.