UAT-UK SPEC CODE: P7 (Radioactivity)ASSUMED MATHS 1 PREREQUISITE: M2.6FREQUENCY: VERY HIGH
Nuclear Decay Chains (α, β⁻, γ), Isotope Algebra & Background-Corrected Half-Life Calculus
Deconstructed from 40 past UAT-UK questions (17.17% of all historical Physics papers). Students using standard A-Level classroom methods spend an average of 130s on this archetype—blowing past the 90s ESAT budget. Using the 2-line Sub-90 heuristic below compresses solve time to 30s (saving 100s per question).
Historical Frequency
40 Past Qs
17.17% of Physics
Classroom Trap Time
130s
+40s over 90s budget
Sub-90 Target Time
30s
Banks +100s on the clock
Dominant UI Format
5-Option A–E
Maths 1 Skill: M2.6
Card 1 & Card 2 Preview: The Classroom Time Trap vs. Sub-90 2-Line Rule
Excerpted from our interactive 6-Step Topic Lesson for ARCH-P-12.
CARD 1 OF 6 • THE CLASSROOM TIME TRAP (130s)
Why Students Bleed Time:
Conservation of nucleon number gives . Conservation of proton number gives (~110s).
In 40 past UAT-UK questions (17.17% of Physics), candidates lose 100s by applying exponential decay (1/2)^n to constant background radiation. Instead, apply P7 with Maths 1 skill M2.6.
CARD 2 OF 6 • THE 2-LINE SUB-90 HEURISTIC (<30s)
**Line 1 (Mass Number ):** Only changes : .
**Line 2 (Proton Balance ):** drops from to ; reaching requires (20s).
Sanity & Limit Check: Verify units/signs against
fence_post_or_domain_trap (Halving the raw detector count rate without subtracting background radiation first (or forgetting to add background back at the end)) and sign_or_direction_flip (Decreasing atomic number Z by 1 instead of increasing Z by 1 in beta-minus (β⁻) decay).Examiner Distractor Blueprint for ARCH-P-12
FOIL #1fence_post_or_domain_trap
Halving the raw detector count rate without subtracting background radiation first (or forgetting to add background back at the end)
Applying exponential decay (1/2)^n to constant background radiation.
FOIL #2sign_or_direction_flip
Decreasing atomic number Z by 1 instead of increasing Z by 1 in beta-minus (β⁻) decay
Confusing β⁻ decay (n -> p + e⁻, so Z -> Z + 1) with Z -> Z - 1.
FOIL #3intermediate_stop_trap
Outputting the remaining parent fraction (1/2)^n instead of daughter nuclei formed N₀ * (1 - (1/2)^n) + N_daughter_initial
Confusing undecayed parent nuclei remaining with total daughter nuclei accumulated.
FOIL #4factor_of_two_or_stoichiometry_trap
Finding number of alpha decays n_alpha = ΔA/4 and subtracting n_alpha from Z instead of 2*n_alpha
Forgetting that each alpha particle carries 2 protons (ΔZ = -2 per alpha).
Try 1 Live Sample Question Under the 90-Second Stopwatch
Press W to open the 2-line dry-wipe scratchpad, select A–E, and lock in to reveal the Dual-View solution.
sub90 ESATARCH-P-12: Nuclear Decay Chains (α, β⁻, γ), Isotope Algebra & Background-Corrected Half-Life Calculus (Sample)Physics
00:00.0
SUB-90 ZONE (<30S)
0.0s30s Sub-9090s ESAT Budget150s Classroom
Right-click any option to cross out • Keys
A–E + EnterQuestion 1 of 1 • 90s Target
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Physics•ARCH-P-12•Standard 5-Option
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