Physics · Modern Physics / Principles and Exploration
Radioactive decay and half-life — principles and investigation
Although we cannot know when a single atom will decay, the overall decay of many atoms appears to be regular. Compare the random decay and exponential decay curves by changing the initial number of atoms, half-life, and initial random number. Half-life is not the time for all atoms to disappear, but the proportion of remaining atoms.
How does it work?
Each decay is random, but the number of atoms remaining decreases exponentially.
N(t) = N₀ (1/2)^(t/T)
Try this investigation
- Each atom collapses at a time drawn from the exponential distribution. The same initial values and conditions produce the same results. Each dot represents a group of atoms, and the number is calculated as the total number of atoms. The counting sound is produced in proportion to the decay rate.
- Press the standard conditions button, run it, and record each measurement value.
- Compare the half-life T records and the curves at 2T and 3T. If you change the initial value, the individual collapse point will change. The speed does not affect the physics results.
Interpreting your results
Why does the difference from the theoretical curve seem large when the number of atoms is small?
Because it is an independent random decay, small samples have large relative errors, and large samples approach the theoretical curve.
Assumptions and limitations
Assume that all atoms have the same constant probability of decay and are independent of each other. The chain decay of daughter nuclides, detector efficiency, and background radiation are omitted. The dots and counting sounds are a shortened version. Random numbers are seed-based pseudorandom numbers.