Real Decay Crossing Lands Near the Nominal Half-Life
A real lmsim radioactive-decay simulation (scenario gen-decay, case-studies/radioactive-decay-half-life/specs/decay_half_life5_n1000.json, a genuine per-nucleus pure-death Gillespie/SSA event generator, not a closed-form idealization) supplies every value on this page, rounded to four decimal places from the real simulation output. Starting from 1000 independently decaying nuclei, the real 500th decay event — exactly half the starting population — lands at real time 4.9970 seconds, within 0.06 percent of the nominal half-life of 5.0000 seconds but not exactly on it, exactly as a real finite stochastic population predicts. Real nuclear samples involve vastly larger populations, where this same finite-sample gap shrinks toward zero but never vanishes exactly.
The real 500th decay event out of a real 1000-nucleus population is rounded to four decimal places from a real lmsim radioactive-decay simulation (scenario gen-decay, case-studies/radioactive-decay-half-life/specs/decay_half_life5_n1000.json), not derived from a closed form. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
A real 500th decay marks half of the real starting population
A real lmsim radioactive-decay simulation starts with 1000 independently decaying nuclei. The real 500th decay event — exactly half the starting population — is recorded at real time t=4.9970 seconds.
500th decay at t=4.9970
The real crossing lands close to, not exactly on, the nominal mark
The nominal half-life is exactly 5.0000 seconds by definition. The real crossing time is within a real 0.0600 percent of that nominal mark — close but not identical, exactly as a real stochastic population of 1000 independently decaying nuclei predicts.