Radioactive Decay Formula
Exponential decay of nuclei with time
Equations
N = N0 e^(−λ t)
λ = ln(2) / t_1/2
N0 is initial quantity; N is remaining after time t; λ is the decay constant; t_1/2 is half-life.
Example
Given: t_1/2 = 5.0 h, N0 = 120 mg, t = 8.0 h.
λ = ln(2)/5.0 = 0.1386 h^-1
N = 120 e^(−0.1386 × 8.0) = 120 e^(−1.1088) ≈ 39.9 mg
Answer: ≈ 39.9 mg remaining after 8 h
Common Mistakes
Wrong units
Match time units for λ and t; use consistent hours, seconds, etc.
Using percent incorrectly
Work with absolute quantities or fractions; convert to percentages at the end.