Lesson 5: Radioactive Decay & Half-Life

Lesson at a Glance | He Tirohanga Whakamua

Do NowWhy Carbon-14 dating works for ancient kauri timber but fails for dinosaur bones10 min

Nuclear Decay EquationsBalancing Alpha (

_{2}^{4} He

), Beta (

_{- 1}^{0} e

), and Gamma (

_{0}^{0} γ

) equations15 min

Half-Life KineticsSolving

N = N_{0} (\frac{1}{2})^{t / t_{1 / 2}}

and exponential decay graphs15 min

Portfolio EntryWrite Section 5: Nuclear Decay Kinetics & Radioactivity Guide10 min

Exit DrillBalance Uranium-238 alpha decay into Thorium-2345 min

Ngā Whāinga Ako | Learning Intentions

Students will know

How to balance Nuclear Decay Equations enforcing conservation of Nucleon Number ( $A$ ) and Charge ( $Z$ ):
• Alpha ( $α$ ): $_{92}^{238} U \to_{90}^{234} Th +_{2}^{4} He$
• Beta Minus ( $β^{-}$ ): $_{6}^{14} C \to_{7}^{14} N +_{- 1}^{0} e + {\bar{ν}}_{e}$
• Beta Plus ( $β^{+}$ ): $_{6}^{11} C \to_{5}^{11} B +_{+ 1}^{0} e + ν_{e}$
The exponential law of Half-Life ( $t_{1 / 2}$ ): $N (t) = N_{0} {(\frac{1}{2})}^{\frac{t}{t_{1 / 2}}}$ .
Applications in radiocarbon dating ( $^{14} C, t_{1 / 2} = 5730 yrs$ ) and medical isotopes.

Students will demonstrate

By calculating remaining activity and sample age for a 22,920-year-old archaeological wood artifact.
By completing Section 5 of their Level 3 Modern Physics Mastery Portfolio.

Do Now | Tīmatanga Whakaaro (10 min)

Radiocarbon Half-Life Prompt:

"Carbon-14 has a half-life of 5,730 years. If a piece of swamp kauri excavated from a Northland peat bog contains exactly 12.5% of its original Carbon-14 activity, how old is the timber?"

Unpack: $12.5 % = \frac{1}{8} = {(\frac{1}{2})}^{3}$ . This means exactly 3 half-lives have elapsed! Age $= 3 \times 5730 years = 17, 190 years old$ .

Radioactive Decay Modes & Kinetics (15 min)

1. Decay Modes Summary

$α$ ( $_{2}^{4} He$ ): Heavy nuclei, paper stopped.
$β^{-}$ ( $_{- 1}^{0} e$ ): High $n / p$ ratio, aluminium stopped.
$γ$ ( $_{0}^{0} γ$ ): High energy photon, thick lead stopped.

2. Half-Life Formula ( $N = N_{0} (0.5)^{n}$ )

Number of half-lives $n = \frac{t}{t_{1 / 2}}$ . Activity $A = λ N$ decays at the exact same exponential rate as particle count.

📁 Physics Modern Portfolio — Section 5: Nuclear Decay Kinetics

Students open their Level 3 Physics Portfolio and complete Section 5:

Section 5 Requirements:

1. Decay Series Diagram: Draw a $(Z vs N)$ Segrè chart illustrating Uranium-238 alpha and beta minus decay steps down to stable Lead-206.

2. Radiocarbon Dating Solver: Calculate remaining mass of a 100g Iodine-131 medical sample ( $t_{1 / 2} = 8.0 days$ ) after 24 days.

3. Excellence Neutrino Conservation Rationale: 1-paragraph explanation of why Wolfgang Pauli postulated the antineutrino ( ${\bar{ν}}_{e}$ ) to conserve momentum and continuous beta energy spectra in $β^{-}$ decay.

Exit Verification | Ka Mutu Hoki (5 min)

Exit Check:

"My Section 5 calculates remaining Iodine-131 mass as 12.5g after 3 half-lives (24 days) and balances Uranium-238 alpha decay into Thorium-234."

Teacher Planning & NCEA Alignment

NCEA Level 3 Physics Alignment (3 Credits Internal):

Radioactive Decay: Demonstrate understanding of alpha, beta minus, beta plus, and gamma decay equations, conservation laws, half-life ( $t_{1 / 2}$ ), and exponential decay graphs.
Conservation Principles: Enforce conservation of nucleon number, charge, mass-energy, and momentum.

Vocabulary: Alpha decay ( $α$ ), beta minus ( $β^{-}$ ), beta plus ( $β^{+}$ ), gamma ( $γ$ ), half-life ( $t_{1 / 2}$ ), decay constant ( $λ$ ), radiocarbon dating, antineutrino.

Other teaching approach: Guided Viewing & Problem Practice →

Lesson 5: Radioactive Decay Series & Half-Life Physics