Foundations — Radioactive decay — alpha, beta, gamma — mechanisms

Before you can read the parent note Radioactive decay — alpha, beta, gamma — mechanisms, you must own every symbol it throws at you. This page builds each one from nothing — plain words, then a picture, then why the topic needs it. Read top to bottom; every idea leans on the one above it.

1. The nucleus, and what it is made of

Picture a nucleus as a tight little cluster of balls. Some balls are protons (they carry positive electric charge), and some are neutrons (they carry no charge — they are electrically neutral, hence the name).

2. $Z$ — the proton counter (atomic number)

• Picture: count the magenta balls in the figure above — that count is $Z$.
• Why the topic needs it: $Z$ decides which element you are. $Z=6$ is always carbon, $Z=92$ is always uranium. When a decay changes $Z$, the atom turns into a different element. Charge conservation (rule 1 of the parent note) is really "the total $Z$ on the left equals the total $Z$ on the right."

3. $A$ — the nucleon counter (mass number)

$A=Z+N(N=\text{number of neutrons})$

• Picture: count all the balls, magenta and violet — that total is $A$.
• Why the topic needs it: $A$ tracks the "bulk" of the nucleus. When a chunk is thrown out (alpha decay), $A$ drops. When a neutron just flips into a proton (beta decay), $A$ stays the same because you still have the same number of balls. Nucleon-number conservation (rule 2) says the total $A$ can never change across the arrow.

4. The isotope notation ${}_Z^{A}X$

Read ${}_{92}^{238}\text{U}$ as: "uranium, 92 protons, 238 nucleons total" — so it has $238-92=146$ neutrons.

5. The Greek letters $\alpha$, $\beta$, $\gamma$ and $\nu$

These are just names, borrowed from the Greek alphabet, for the three kinds of "stuff" a nucleus emits — labelled in the historical order they were discovered (first, second, third letter).

• Why the topic needs them: these four symbols are the entire cast of decay products. Every decay equation in the parent note is built from $X$, $Y$, and one of $\alpha ,\beta ,\gamma ,\nu$.

6. Electron $e$, charge $e$, and the symbol clash

The letter $e$ is overloaded — beware:

• $e^{-}$ = the electron particle (tiny, negative).
• $e^{+}$ = the positron, its positive antimatter twin.
• a bare $e$ inside "$+2e$" or "$-e$" means the size of one proton's charge — a unit of charge, not a particle.

So "the alpha has charge $+2e$" means "twice the proton charge," because an alpha holds 2 protons. The topic needs this because charge is measured in multiples of $e$, and that is how the comparison table lists charges.

7. Energy, mass, and the bridge $E=m{c}^2$

Why the topic needs it: the parent note claims "products are lighter than the parent, and the missing mass becomes kinetic energy." That sentence is only meaningful because of $E=m{c}^2$ — missing mass is released energy. This is the same idea explored in Nuclear binding energy and mass defect.

8. Kinetic energy $KE$ and momentum $p$

For an object of mass $m$ moving slowly compared to light, these two are linked by:

$KE=\frac{p^2}{2m}$

9. The Q-value — the "energy budget"

• Picture: put the parent on one pan of a scale and all its products on the other. If the products are lighter, that missing weight — times $c^2$ — is the energy handed out as motion.
• Why the topic needs it: $Q$ is the single number that answers "will it decay, and how much energy comes out?" Every worked example computes kinetic energies as fractions of $Q$.

10. Discrete vs continuous spectra

Why the topic needs it: this single distinction is the fingerprint that separates the decays. Alpha and gamma give discrete lines (two-body split → fixed shares). Beta gives a continuous band, because a third particle (the neutrino) secretly shares the energy differently each time — that continuous shape is the historical clue that forced the neutrino's existence. See Neutrino and lepton number conservation.

11. Two words you will meet: "excited state" and "half-life"

12. Two mechanisms named in the table

You do not need to master these yet, but recognise the names:

• Quantum tunnelling — a particle "leaking" through a wall it classically could not cross. This is how an alpha escapes: Quantum tunnelling.
• Weak interaction — the fundamental force that flips a neutron into a proton (and vice-versa) and creates the electron + neutrino. This is how beta decay happens: Weak interaction.

Prerequisite map

Equipment checklist

Test yourself — cover the right side. If any answer is fuzzy, reread that section before opening the parent note.