Radioactive Decay (Copy)
- Radioactive decay is:
- Spontaneous: unaffected by external conditions like pressure, temperature, or chemical changes
- Random: cannot predict which nucleus decays next, only probability over time
Key Definitions
- Activity (A):
A = λN- A = activity in becquerels (Bq)
- λ = decay constant (s⁻¹)
- N = number of undecayed nuclei
- Decay Constant (λ):
- Probability per unit time that a nucleus will decay
- Larger λ means faster decay
- Half-life (t₁₋₂):
λ = 0.693 / t₁₋₂- Time taken for half the radioactive nuclei to decay
Exponential Decay Equations
- Number of undecayed nuclei:
N = N₀e⁻ˡᵃᵐᵇᵈᵃᵗ - Activity:
A = A₀e⁻ˡᵃᵐᵇᵈᵃᵗ - Count rate:
x = x₀e⁻ˡᵃᵐᵇᵈᵃᵗwhere:
- N₀, A₀, x₀ = initial values
- t = time
Example Calculations
Example 1:
If λ = 2.0 × 10⁻³ s⁻¹, then:
t₁₋₂ = 0.693 / 2.0 × 10⁻³ = 346.5 s
Example 2:
A₀ = 1000 Bq, λ = 0.001 s⁻¹, t = 500 s
A = 1000 × e⁻⁰·⁵ ≈ 606.5 Bq
Graph Shape
- N, A, or x vs time:
- Exponential curve
- Never touches zero
- Decays slowly over time
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course