7.74PH1 · Section 7: Radioactivity and particles

Radioactive decay equations

Key learnings

Balance A and Z on both sides
Every nuclear equation obeys two exact conservation laws. Mass number $A$ (top): the sum on the left equals the sum on the right. Atomic number $Z$ (bottom): the left sum equals the right sum; a change in $Z$ means a different element. Include the emitted particle: alpha ( $A=4, Z=2$ ), beta-minus ( $A=0, Z=-1$ ), gamma ( $A=0, Z=0$ ), neutron ( $A=1, Z=0$ ). To find a missing nuclide, balance $A$ and $Z$ by subtraction, then read the element from $Z$ .
Effect of each decay on A and Z
Alpha (α): $A$ falls by 4, $Z$ falls by 2 (emits $^4_2\text{He}$ ). Beta-minus (β⁻): $A$ unchanged, $Z$ rises by 1 — a neutron converts to a proton, emitting $^0_{-1}\text{e}$ . Gamma (γ): $A$ and $Z$ both unchanged — the nucleus just releases energy as a photon. Neutron emission: $A$ falls by 1, $Z$ unchanged. Worked (alpha): $^{238}_{92}\text{U} \rightarrow ^{234}_{90}\text{Th} + ^4_2\text{He}$ — check $A$ : $238 = 234 + 4$ ; $Z$ : $92 = 90 + 2$ .
Nuclide notation and finding the element
In $^A_Z\text{X}$ : $A$ = mass number (top-left), $Z$ = atomic number (bottom-left); the symbol X is fixed by $Z$ , not $A$ . Isotopes = same $Z$ , different $A$ . After a decay, look up the new $Z$ on the periodic table — do not guess. Useful values: $Z=82$ Pb, $84$ Po, $86$ Rn, $88$ Ra, $90$ Th, $92$ U. Beta-minus mechanism: $^1_0\text{n} \rightarrow ^1_1\text{p} + ^0_{-1}\text{e}$ , so $Z$ rises by 1 while $A$ stays the same.

Common mistakes

Drawn from real examiner reports.

Balance BOTH A and Z

The commonest slip is balancing only one row. Some recall that alpha decay drops $Z$ by 2 but never fix $A$ . Do a two-step check: sum the top ( $A$ ) numbers on each side — they must match — then sum the bottom ( $Z$ ) numbers. For a missing nuclide: missing $A$ = (left $A$ sum) − (known right $A$ ); missing $Z$ likewise; then find the element from $Z$ .

November 2024 Paper 2P Q1 — candidates recalled alpha decay reduces proton number by 2 but could not balance the complete equation; the examiner emphasised that BOTH top and bottom numbers must balance.

Half-life: it's the nuclei that halve

"Time for radiation/radioactivity to halve" is imprecise. The mark scheme wants the time for half the radioactive nuclei in a sample to decay (the activity halves as a consequence). Never write "time for the material to disappear" — a sample does not vanish after one half-life. Refer to nuclei, and to a fixed time period.

November 2024 Paper 1P Q4(c)(i) — weaker candidates gave imprecise descriptions of what is being halved in a half-life definition, losing at least one mark.

Look up the daughter symbol from Z

After finding the new $Z$ , use the periodic table for the element symbol — do not reuse the parent's symbol. E.g. uranium ( $Z=92$ ) alpha-decays to thorium (Th, $Z=90$ ), not "U". Also do not swap the symbol positions ( $^Z_A\text{X}$ ) or keep $Z$ the same for beta-minus (where $Z$ rises by 1).

November 2024 Paper 2P Q1 — candidates who correctly recalled the proton number change from alpha decay failed to write the correct daughter nucleus symbol.

Alpha Z−2 vs beta-minus Z+1

Mix up the direction and you get the wrong element. Alpha: $Z$ falls by 2 (daughter 2 places left in the periodic table). Beta-minus: $Z$ rises by 1 (1 place right), because a neutron becomes a proton. $A$ falls by 4 for alpha but is unchanged for beta-minus.

A goes on top, Z on the bottom

In the nuclide symbol the mass number $A$ is top-left and the atomic number $Z$ is bottom-left. Writing $^Z_A\text{X}$ (swapped) or leaving $Z$ off the daughter loses marks. The bigger number is $A$ and sits on top; the smaller number is $Z$ below.

Beta-minus symbol: charge is −1

The beta-minus particle is written $^0_{-1}\text{e}$ (charge $-1$ ), NOT $^0_{+1}\text{e}$ (that is a positron). It is created when a neutron converts to a proton inside the nucleus — it is not an electron from a shell. Getting the $-1$ charge and the nuclear origin right is needed for full marks.

Exam tips

Four-step equation scaffold
(1) Write the parent and known particles. (2) Missing $A$ = left $A$ − known right $A$ . (3) Missing $Z$ = left $Z$ − known right $Z$ . (4) Look up $Z$ for the element symbol. Works for any decay type. E.g. $^{226}_{88}\text{Ra}$ alpha decay → $A=222$ , $Z=86$ → Rn.
Always run the balance check
After writing an equation, verify BOTH rows: the top ( $A$ ) numbers sum equally on each side, and the bottom ( $Z$ ) numbers sum equally. Checking only one row is the classic way to leave an error in place.
Get the element from Z, not the parent
Never copy the parent's symbol onto the daughter. Compute the new $Z$ , then read the element from the periodic table. A wrong symbol loses the mark even when your $A$ and $Z$ values are correct.
Working backwards? Add, don't subtract
If the daughter is given and you need the parent, remember parent = daughter + emitted particle, so you ADD: for alpha, $A_\text{parent} = A_\text{daughter}+4$ and $Z_\text{parent} = Z_\text{daughter}+2$ . Subtracting here is a common slip.

Revision notes