Disintegration Rates and Half-Lives

Note that the rate is represented as a negative quantity since the number of atoms must decrease as time progresses, The constant X is called the decay constant of the isotope end is independent of temperature, pressure, or state of combination of the element. Generally, we are interested in the number of disintegrations that occur over a finite time, and equation (7) becomes most useful in its integrated form. In particular, workers very often refer to the half-life period of an isotope—that is, the time required for just one half of the atoms of that type in a sarnpie to decay. If we call this time Ti/-2, n may be shown (Exercise 2) that  

Naturally occurring radioactive elements must have half-life periods comparable to or greater than the age of the earth (several billion years) or else must be constantly regenerated by natural processes. 

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