Each nucleus decays at random: you cannot say which will go next, only the probability per second, the decay constant λ. Yet over a whole sample the numbers follow a smooth exponential, N = N₀e⁻λᵗ, halving every half-life. Watch the individual nuclei wink out while the count curve traces the maths.
MissionWatch the count fall to half after one half-life, then to a quarter after two, however large the half-life.Streak 0Best 0
The decay constant λ and the half-life t½ are related by:
nuclei remaining N120
decay constant λ = 0.693/t½0.069 s⁻¹
activity A = λN8 s⁻¹
elapsed time0.0 s
Decay is random and spontaneous, but a large sample halves in a fixed half-life, giving the exponential law.