PYQ Vault

Playbook

Nuclei

Mass defect, binding energy and Q-values. Radioactivity has almost stopped appearing, so the binding-energy pages now carry the chapter.

Questions in the bank
97
q/paper in 2025–26
0.52
Numeric answer
24%
Notes pages
4

Tier: Long tail

When you’ll see it

A nuclear radius, a mass defect or binding energy, the energy a reaction releases, or a decay and its half-life.

How this chapter is tested

The questions the recent papers set are on three ideas: the nuclear radius, binding energy from a mass defect, and the energy a reaction releases. Every nucleus has the same density, and a reaction releases the gain in binding energy.

Radioactivity was cut from the syllabus, and it has almost stopped appearing: decay modes, half-lives and decay constants are rare in the recent papers. Those pages serve the older papers more than the next one.

Marks are lost on bookkeeping: a binding energy per nucleon not multiplied by A, the alpha's recoil share forgotten, or the fraction decayed read as the fraction left. Energies in MeV and mass-energy conversion are shared with Atoms and Dual Nature.

The sub-skills

The distinct skills inside the chapter, in the order to learn them.

  • Nuclear size and binding energy

    R = R₀A^(1/3), so every nucleus has the same density; the mass defect times c² is the binding energy, and stability is judged per nucleon, which peaks near iron.

  • Q-value, fission and fusion

    Q is the gain in total binding energy, or the mass lost times c²; in alpha decay the alpha takes Q(A − 4)/A; a sample's energy is Q times the number of reactions.

  • Decay modes and half-lives

    Alpha takes 4 from A and 2 from Z, beta-minus adds 1 to Z, beta-plus takes 1 away; each half-life halves what is left.

  • Decay constant and activity

    N = N₀e^(−λt), half-life ln 2/λ, mean life 1/λ, activity λN; two decay routes add their λ's.

Traps to expect

Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.

  • Per nucleon not multiplied by A

    Binding energies per nucleon cannot be subtracted directly. Multiply each by its own A, then subtract the totals.

  • The sign of Q

    With binding energies Q = after − before; with masses Q = before − after. Mixing the two flips the sign.

  • The alpha's share

    Momentum is shared equally and oppositely, so the alpha gets Q(A − 4)/A, not all of Q.

  • Decayed read as left

    If 15/16 has decayed, 1/16 is left and four half-lives have passed. Taking the decayed fraction as the fraction left gives a time far too short.

Learn it before you drill it

This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each page. Read the notes once, then drill page by page below.

Nuclei notes

Drill every Nuclei question

97 questions from the bank, across 4 subtopics.

Drill the 97 questions

Drill one subtopic at a time

The 4 subtopics, in teaching order.

Related playbooks

Often paired with this one — the technique or the trap overlaps. Drill these next.