Radioactive Decay • Radioactive decay is the process where an unstable atomic nucleus loses energy by emitting radiation. • Occurs randomly but follows a predictable statistical pattern described by exponential decay. • Types of radioactive decay: – Alpha decay (α) – Emission of a helium nucleus (42 He), reducing atomic number by 2 and mass number by 4. – Beta decay (β − or β + ) – Neutron converts into a proton or vice versa, emitting an electron or positron. – Gamma decay (γ) – Emission of high-energy photons without changing the atomic number. Radioactive Decay Law • Follows an exponential decay model: N (t) = N0 e−λt (1) • Variables: – N (t) – Number of undecayed nuclei at time t. – N0 – Initial number of nuclei. – λ – Decay constant (probability of decay per unit time). – t – Time elapsed. Half-Life (t1/2) • Time required for half of the radioactive nuclei to decay. • Formula: ln 2 λ (2) 0.693 = 346.5 s 0.002 (3) t1/2 = • Example Calculation: If λ = 0.002 s−1 , t1/2 = Activity and Decay Rate • Activity (A) represents the number of decays per second. • Given by: A = λN (4) • Activity decreases exponentially over time: A = A0 e−λt • Measured in Becquerels (Bq), where 1 Bq = 1 decay per second. 1 (5) Energy and Radiation Effects • Alpha particles (α): – Heavy and low-penetrating (stopped by paper/skin). – Dangerous if inhaled or ingested. • Beta particles (β − or β + ): – Medium penetration (stopped by plastic/aluminum). – Can cause skin burns if exposure is high. • Gamma rays (γ): – High-energy electromagnetic radiation. – Highly penetrating (requires lead/concrete shielding). Radioactive Dating • Used to determine the age of objects by measuring isotope decay. • Common methods: – Carbon-14 dating – Used for organic materials (half-life: 5,730 years). – Uranium-Lead dating – Used for geological samples (half-life: billions of years). • Works by comparing the ratio of parent to daughter isotopes. Mathematical Application in Radioactive Decay • To determine how much of a radioactive sample remains after a given time, use: N = N0 e−λt (6) • If given a half-life, the decay constant can be found by: λ= ln 2 t1/2 (7) • Example: A sample has a half-life of 10 hours. Find the decay constant. λ= 0.693 = 0.0693 hr−1 10 Health Effects and Safety Measures • Radiation exposure is measured in Sieverts (Sv). • Effects of exposure: – <0.1 Sv: No noticeable effects. – 0.1 - 1 Sv: Increased cancer risk. 2 (8) – Above 5 Sv: Radiation sickness and fatality risk. • Protection from radiation: – Distance: Increasing distance from the source reduces exposure. – Shielding: Using lead/concrete to block gamma radiation. – Time: Reducing exposure duration limits total dose received. 3