Nuclei and Nuclear Energy

Lesson

Part 1 — what a nucleus is made of, how big and how dense it is, and where its binding energy comes from.

In this lesson you will

Describe the composition of a nucleus, classify isotopes, isobars and isotones, and use R = R₀A^(1/3) to find nuclear size and show that nuclear density is the same for all nuclei
Use the unified atomic mass unit and E = mc² to calculate mass defect and binding energy in MeV
Explain pair production and annihilation and calculate the energies involved

Concept

What is inside a nucleus

A nucleus contains protons (charge +e) and neutrons (no charge), together called nucleons. A nuclide is written $^{A}_{Z}\text{X}$ , with $A = Z + N$ .

Z is the atomic number (protons), N the neutron number, A the mass number (nucleons).
The number of electrons in the neutral atom is Z, so Z decides the chemical element.
Protons repel one another electrically; the short-range strong nuclear force holds the nucleons together.

Table of atomic number, neutron number and mass number, each with its symbol, meaning and its value for sodium-23
Quantity	Symbol	Meaning	Example: ²³₁₁Na
Atomic number	Z	Number of protons	11
Neutron number	N	Number of neutrons, N = A − Z	12
Mass number	A	Number of nucleons, A = Z + N	23
Nuclide symbol	²³₁₁Na	A written above Z, before the element symbol	sodium-23

Diagram

Isotopes, isobars and isotones

Table of isotopes, isobars and isotones: what is the same and what differs, with an example pair for each
Name	Same	Different	Example pair
Isotopes	Z (protons)	N and A	³⁵₁₇Cl and ³⁷₁₇Cl
Isobars	A (nucleons)	Z and N	⁴⁰₁₈Ar and ⁴⁰₂₀Ca
Isotones	N (neutrons)	Z and A	³₁H and ⁴₂He

Nuclides are grouped by what they share:

Isotopes: same Z, different A (same element, same chemistry), such as carbon-12 and carbon-13.
Isobars: same A, different Z, such as carbon-13 and nitrogen-13.
Isotones: same N, different Z, such as carbon-12 and nitrogen-13.

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