Carbon dating exercises

The number at the top is how many half-lives have elapsed.

Note the consequence of the law of large numbers: with more atoms, the overall decay is more regular and more predictable.

Perhaps a puddle of a certain size will evaporate down to half its original volume in one day.

But on the second day, there is no reason to expect that one-quarter of the puddle will remain; in fact, it will probably be much less than that.

Consider a mixture of a rapidly decaying element A, with a half-life of 1 second, and a slowly decaying element B, with a half-life of 1 year.

In a couple of minutes, almost all atoms of element A will have decayed after repeated halving of the initial number of atoms, but very few of the atoms of element B will have done so as only a tiny fraction of its half-life has elapsed.

In such cases, the half-life is defined the same way as before: as the time elapsed before half of the original quantity has decayed.

For example, the medical sciences refer to the biological half-life of drugs and other chemicals in the human body. The original term, half-life period, dating to Ernest Rutherford's discovery of the principle in 1907, was shortened to half-life in the early 1950s.After another 5,730 years, one-quarter of the original will remain.On the other hand, the time it will take a puddle to half-evaporate depends on how deep the puddle is.Rutherford applied the principle of a radioactive element's half-life to studies of age determination of rocks by measuring the decay period of radium to lead-206.Half-life is constant over the lifetime of an exponentially decaying quantity, and it is a characteristic unit for the exponential decay equation.

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