# Radiometric dating parent daughter isotopes

*14-Sep-2017 00:44*

When plants absorb carbon-dioxide in the photosynthesis process, some of the carbon dioxide has the carbon-14 atom in the molecule.

Assuming that our atmosphere's composition and the cosmic ray flux has not changed significantly in the last few thousand years, you can find the age of the organic material by comparing its carbon-14/carbon-12 ratios to those of now-living plants.

The number of *parent* *isotopes* decreases while the number of *daughter* *isotopes* increases but the total of the two added together is a constant.

You need to find how much of the **daughter** **isotopes** in the rock (call that isotope ``A'' for below) are the result of a radioactive decay of **parent** atoms.

There are always a few astronomy students who ask me the good question (and many others who are too shy to ask), ``what if you don't know the original amount of **parent** material?

() is the ``natural logarithm'' (it is the ``ln'' key on a scientific calculator).

Different *isotopes* of a given element will have the same chemistry but behave differently in Radioactive *isotopes* will decay in a regular exponential way such that one-half of a given amount of *parent* material will decay to form *daughter* material in a time period called a half-life. When the material is liquid or gaseous, the *parent* and *daughter* *isotopes* can escape, but when the material solidifies, they cannot so the ratio of *parent* to *daughter* *isotopes* is frozen in.

The *parent* isotope can only decay, increasing the amount of *daughter* *isotopes*. The number n is the number of half-lives the sample has been decaying.

All atoms of an element have the same number of protons in their nucleus and behave the same way in reactions.

The atoms of an isotope of a given element have same number of protons AND neutrons in their nucleus.

Radioactive *dating* gives the Find out how many times you need to multiply (1/2) by itself to get the observed fraction of remaining *parent* material. If some material has been decaying long enough so that only 1/4 of the radioactive material is left, the sample is 2 half-lives old: 1/4 = (1/2) × (1/2), n =2.