Random decay and half-life sim
Count background, shake a protactinium generator, record 10 s counts with a GM tube, plot the corrected decay curve, read and average the half-life, then watch 400 model nuclei decay at random.
Radioactivity · covers the O-Level, IGCSE, GCSE topic
What the sim shows
Radioactive decay is random and spontaneous: you can't tell which nucleus will decay next, or when, and nothing you do changes it. A Geiger–Müller tube always picks up background radiation (about 30 counts a minute here, from rocks, buildings, the air and space). Subtract it, converted to the same counting time (÷ 6 for 10 s counts): corrected count = count − background per minute ÷ 6. Shaking the sealed protactinium generator moves protactinium-234m into the colourless top layer. Its activity then follows A = A₀ × (½)^(t ÷ t½) with t½ = 70 s, so the count rate halves every 70 s however high it starts, and the half-life can be read from any halving on the graph; averaging several gives a better value. After three half-lives one eighth is left. Each count is a random (Poisson) number whose spread is about √count. So late, small counts scatter less in counts (about ±6 at 36, against about ±24 at 576) but more as a fraction of the count (√N ÷ N = 1 ÷ √N: about 17 % at 36, against about 4 % at 576), which makes them the least reliable as a fraction; the readout shows each count beside the value expected on average. The grid model shows the same thing: every nucleus has the same chance p of decaying in each step (1 in 6 for the dice, so the number left halves about every 3.80 throws; for protactinium-234m p = 1 − 2^(−10 ÷ 70) = 0.0943 per 10 s). Model limits: time only moves on when you count, and counts are played back faster than real time (10 s in about 2 s). Each point is plotted at the middle of its 10 s count. The tube reads only the top layer (the bottom layer's own activity is ignored), the "away" position is taken to read background only, the tube loses about 0.6 % of counts to its dead time (100 µs), and a real generator needs about 10 minutes before it can be used again. Real nuclei can't be seen: the grid's colours are only a model. Safety: sealed sources are moved with tongs, kept in a tray, held away from the body and used for the shortest time, and the generator is never opened.
- GM tube end window: thin mica, so beta particles get in
- Generator: pale-yellow uranium salt solution under a colourless organic layer
- Graph: your halvings, from N down to N/2
Use it in your lessons
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