Radioactive Decay Law — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Radioactive Decay Law Applies to a large collection of radioactive nuclei undergoing random, spontaneous disintegration obeying statistical laws. Rate of decay is proportional to number of undecayed nuclei: dN/dt = - N Rearrange: dN/N = - dt Integrate from N 0 to N and 0 to t ln(N) - ln(N 0) = - t Take exponential of both sides: N = N 0 e - t Valid only for a large number of nuclei (statistical nature). Not applicable to a single nucleus. Decay constant lambda is independent of external physical and chemical conditions. Thinking N is the number of decayed nuclei. Believing rate of decay is constant. Confusing half-life with mean life.