PHY063 · Modern Physics · Class 12 + College
Half-life
Objective: To understand half-life: the time for half of the remaining nuclei to decay.
🧰 Apparatus
- (Digital only) decay simulation
- 100 coins or dice
- Tray
- Graph paper
📐 Formulas and SI units
t½ = ln 2 / λ = 0.693 / λ
N = N₀ (½)^(t/t½)
💡 Theory
In each half-life t½ the number of nuclei halves, whatever the starting number: 100% → 50% → 25% → 12.5%. Half-life is linked to the decay constant by t½ = ln 2/λ ≈ 0.693/λ. Half-lives range from microseconds to billions of years.
🪜 Procedure
- Set λ and read the half-life.
- Watch the bars halve at each half-life.
- Coin model: toss 100 coins, remove the heads, and repeat; count the throws for half to go.
- Compare the coin 'half-life' with the theory (1 throw).
📋 Observations Simulated values
✅ Result and conclusion
λ = 0.0693 /s gives t½ = 10 s; after 3 half-lives (30 s) 12.5% remains.
🔬 In a real lab
With few nuclei (or coins) the halving is irregular; averaging several runs gives a better half-life.
⚠️ Safety
This experiment is digital only; no radioactive material is handled. Coins and dice are safe models.
❓ Quick check
1. After 2 half-lives, the fraction left is…
2. Doubling λ makes the half-life…
3. Carbon dating uses carbon-14 with t½ ≈ 5730 years because…
🏋️ Practice
Easyt½ = 5 min. Fraction left after 20 min?
Answer: 1/16
Mediumλ for t½ = 0.693 s?
Answer: 1 /s
Challenge800 nuclei, 3 half-lives later?
Answer: 100