# Formula radiometric dating

*01-Jul-2017 09:39*

In mathematical terms, radioactive decay is governed by a simple exponential formula, taught in many high school math classes: P is the amount after time t, and L is the decay constant for the radioactive isotope.This decay constant L can be expressed in terms of the half life T (the time it takes for one-half of the material to decay) as L = log(2) / T, where log(2) = 0.693147... In other words, if we know P, or even merely their ratio, we can solve the above equation for the time t.However, usually it is not possible to apply this formula directly, because, for instance, in many cases we do not know the original amount of the radioactive isotope when the rock was solidified.Also, such a calculation does not provide us with any statistical error margin to double-check the result.For example, as of the present date, numerous used mass spectrometers are available for sale on e Although most items are priced in the thousands of dollars, prices are dropping.

For example, the rubidium-strontium isochron method, one of the most widely used schemes, is based on the radioactive decay of rubidium-87 into strontium-87 by the emission of a high-energy electron.By some simple algebraic manipulation of the basic radioactivity formula above, one can show that the following formula must hold at any time t: (Sr87/Sr86) is the ratio of these two isotopes at time t.Note that this equation is in the simple form y = b m x, namely the formula for graph of a straight line with slope m and with y-intercept b: here y = (Sr87/Sr86).The half-life T of this decay has been measured in careful laboratory measurements as T = 48.8 billion years.

On the other hand, strontium-86 is a stable isotope.Of course, in real scientific research, scientists do not rely on manually drawing points on graph paper to determine a best-fit straight line or to determine the line's slope or y-intercept.