ARCH-P-12: Nuclear Decay Chains (α, β⁻, γ), Isotope Algebra & Background-Corrected Half-Life Calculus

Full 15-Q Timed Drill

Step 1 of 6 • The Core Idea

ARCH-P-12: Why the 130s Classroom Method Fails Under the 90s Clock

Standard Classroom Method (Too Slow)~130s (Blows 90s Clock)

Conservation of nucleon number gives

222 = 210 + 4 N_\alpha + 0 N_\beta \implies N_\alpha = \frac{222-210}{4} = 3

. Conservation of proton number gives

86 = 82 + 2 N_\alpha - N_\beta \implies N_\beta = 82 - (86 - 2\times 3) = 2

(~110s).

The Fast ShortcutTarget: 30s (Saves 100s)

**Line 1 (Mass Number

\implies \alpha

):** Only

\alpha

changes

A

N_\alpha = \frac{222-210}{4} = 3

.
**Line 2 (Proton Balance

\implies \beta^-

):**

3\alpha

drops

Z

from

86

80

; reaching

82

requires

N_\beta = 82 - 80 = 2

(20s).

Where Students Lose Time: 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.

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