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The particles given off during the decay process are part of a profound fundamental change in the nucleus.To compensate for the loss of mass (and energy), the radioactive atom undergoes internal transformation and in most cases simply becomes an atom of a different chemical element.In other words, the probability of a radioactive atom decaying within its half-life is 50%.For example, the image on the right is a simulation of many identical atoms undergoing radioactive decay.) is the time required for a quantity to reduce to half its initial value.The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo, or how long stable atoms survive, radioactive decay.Because isotopes differ in mass, their relative abundance can be determined if the masses are separated in a mass spectrometer (see below Use of mass spectrometers).

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.

Pursuing this analogy further, one would expect that a new basket of apples would have no oranges but that an older one would have many.

In fact, one would expect that the ratio of oranges to apples would change in a very specific way over the time elapsed, since the process continues until all the apples are converted. A particular rock or mineral that contains a radioactive isotope (or radio-isotope) is analyzed to determine the number of parent and daughter isotopes present, whereby the time since that mineral or rock formed is calculated.

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.

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