Real Decay Half-Life Ledger

Real Decay Crossing Lands Near the Nominal Half-Life

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=4.9970500\text{th decay at }t=4.9970
Real 500th decay vs. the nominal half-lifeThe real crossing of remaining=500 lands near, not on, the nominal half-life.nominal half-life=5.0000 sreal 500th decay t=4.9970 s

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.

4.9970≈5.00004.9970\approx5.0000
Real 500th decay vs. the nominal half-lifeThe real crossing of remaining=500 lands near, not on, the nominal half-life.nominal half-life=5.0000 sreal 500th decay t=4.9970 s