Radioactive Decay Cheat Sheet 1. Exponential Decay Law N (t) = N0 e−λt (1) where: • N (t) = Number of undecayed nuclei at time t • N0 = Initial number of nuclei • λ = Decay constant (s−1 ) • t = Time elapsed (s) 2. Half-Life Formula t1/2 = ln 2 λ (2) where: • t1/2 = Half-life (time for half the substance to decay) • ln 2 ≈ 0.693 3. Activity and Decay Rate A = λN (3) A = A0 e−λt (4) where: • A = Activity at time t (Bq) • A0 = Initial activity (Bq) • λ = Decay constant (s−1 ) 4. Decay Constant from Half-Life ln 2 t1/2 (5) E = hf (6) λ= 5. Energy of Radiation where: • E = Energy of radiation (J) • h = Planck’s constant (6.626 × 10−34 J·s) • f = Frequency of radiation (Hz) 1 6. Radiation Exposure and Safety D= E m (7) where: • D = Radiation dose (Gray, Gy) • E = Energy absorbed (J) • m = Mass of exposed tissue (kg) 7. Calculating Remaining Mass from Decay m = m0 e−λt (8) where: • m = Remaining mass of radioactive substance • m0 = Initial mass • λ = Decay constant (s−1 ) 8. Relationship Between Activity and Mass A = λN = λm M (9) where: • A = Activity (Bq) • λ = Decay constant (s−1 ) • m = Mass of radioactive substance (g) • M = Molar mass (g/mol) 9. Sieverts and Radiation Dose Calculation H = DQ where: • H = Equivalent dose (Sieverts, Sv) • D = Absorbed dose (Gray, Gy) • Q = Radiation weighting factor 2 (10)