Radioactive Decay Law Half Life Form — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Radioactive Decay Law (Half-life form) Applies to large samples of radioactive isotopes undergoing spontaneous decay. Start with the exponential decay law: N = N0 e (-λt). Definition of half-life (T 1/2): At t = T 1/2, N = N0/2. Solve for decay constant: λ = ln(2) / T 1/2. Substitute λ back into the exponential equation: N = N0 e (-[ln(2)/T 1/2] t). Use exponent properties: N = N0 (e ln(2)) (-t/T 1/2) = N0 (2) (-t/T 1/2). Rewrite as N = N0 (1/2) (t/T 1/2). The sample size must be large enough for statistical laws to apply. The decay constant must be independent of physical conditions like temperature or pressure. Thinking that all nuclei will decay in two half-lives; actually, 25% remain after two half-lives. Confusing the number of decayed nuclei with the number of remaining nuclei.