Mean Life Equation — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Mean Life Equation Used in nuclear physics to characterize the stability and lifespan of radioactive isotopes following exponential decay laws. Define mean life as the sum of lives of all nuclei divided by the total number of nuclei. Express total life as the integral from 0 to infinity of t multiplied by the number of nuclei decaying at time t (dN). Substitute dN = lambda N0 e (-lambda t) dt. Evaluate the integral (1/N0) integral[0, inf] (t lambda N0 e (-lambda t)) dt using integration by parts. The result simplifies to 1/lambda. Applies to large populations of nuclei where statistical averages are valid. Assumes the decay constant is independent of the age of the nucleus. Confusion between mean life (tau) and half-life (T 1/2). Mean life is approximately 1.44 times the half-life. Assuming mean life is the time after which exactly half the sample remains (that is half-life).