Radiometric Dating

Is there a way to determine how old a fossil is? What about a rock? How about the earth? Are they under 10,000 years old, or more than 1,000,000,000?

There are several ways to scientifically determine the time when certain entities were formed. In this post, we examine radioactive decay in general. In the following posts, we will take a look at some specific examples of dating methods, such as Isochron Dating. As always, we will be using a skeptical eye to determine whether or not such methods are reliable.

Radiometric Dating for Chemistry Beginners


The first thing one needs to understand radioactive decay is a little basic chemistry. More specifically, we need to understand isotopes. Here is a copy of the Periodic Table of the Elements (if you have trouble reading this copy, then google "periodic table with atomic mass and atomic number").

The periodic table is astoundingly complex and gives us vast amounts of information, but right now we just need to know a few basics.

• The large, bold letters are the symbols of the individual elements. For example, the large "H" at the top-left corner stands for Hydrogen, the "He" at the top-right corner stands for Helium, and the "Li" underneath Hydrogen stands for Lithium.
• The numbers above the symbols are the atomic numbers. The atomic number equals the number of protons that an element contains.
• The number of protons that an element contains defines it's identity. If you change the number of protons, you change the element. (Add a proton to Hydrogen and you get Helium)
• The number below the symbols is the atomic weight.

But what makes up an element's atomic weight? Well, protons, neutrons, and electrons! (electrons are so small that we won't need to take them into account during this discussion)

For our purposes, the atomic weight of an element equals the weight of the protons plus the weight of the neutrons:

Atomic Weight = Protons + Neutrons

The atomic weight of both protons and neutrons is about 1 atomic mass unit (1 amu). So, if an element has 2 protons and 2 neutrons, it has an atomic weight of about 4 amu's. If an element has 6 protons and 7 neutrons, it has an atomic weight of 13 amu's.

2 protons + 2 neutrons = 4 amu's

6 protons + 7 neutrons = 13 amu's

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Now we are ready to take a look at isotopes, which are the basis for radiometric dating. An isotope is a variant of an element. Where does this variation come from? It can't be a variation in the number of protons, because if you change the number of protons you have a different element entirely. What can change is the number of neutrons. So, isotopes of an element have the same number of protons, but differing numbers of neutrons.

Let's take a look at some of the isotopes of carbon.

Carbon-12: has 6 protons and 6 neutrons, and an atomic weight of about 12 amu's

Carbon-13: has 6 protons and 7 neutrons, and an atomic weight of about 13 amu's

Carbon-14: has 6 protons and 8 neutrons, and an atomic weight of about 14 amu's

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There is an extremely important property of Carbon-14: it undergoes radioactive decay. There is much to be said about radioactive decay, but right now all we need to know is that over time, Carbon-14 will turn into Nitrogen-14 (7 protons, 7 neutrons) through beta decay.

The amount of time that it takes for half of the Carbon-14 in a sample to turn into Nitrogen-14 is about 5730 years. Therefore, the half life of Carbon-14 is about 5730 years.

Here is a chart to help understand what takes place after a certain number of half lives have taken place.

Number of Half-Lives Elapsed	Fraction of Isotope Remaining
0	1/1
1	1/2
2	1/4
3	1/8
4	1/16
n	1/(2n)



Here is are a few examples:

• You start out with 50 grams of Carbon-14. How long will it be until there are 25 grams left? Since the half life of Carbon-14 is 5730 years, it will take 5730 years.
• You start out with 50 grams of Carbon-14. How long will it be until there are 13.5 grams left? Since 25 is half of 50, and 13.5 is half of 25, two half lives must have taken place. Therefore, 5730 X 2 = 11460 years.

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Now we have all of the tools necessary to understand the basics of radiometric dating. Once you know 1) the half life of an isotope, 2) the current mass of the sample, and 3) the original mass of the sample, you can determine the age of the sample.

In the case of Carbon-14, we know the half life and the current mass of samples is easily obtainable. The hard part is determining the original mass of the sample.

Fortunately, there is an interesting way to determine the original amounts of Carbon-14 in organic remains. Plants fix carbon from the atmosphere, and the ratio of the isotopes of carbon in the atmosphere remains relatively constant over time (this last sentence is a point of contention, and will be the subject of future posts). Therefore, the ratio of Carbon-14 to Carbon-12 in a living organism is at a set value. When that organism dies, it no longer takes in atmospheric carbon, so the amount of Carbon-14 starts to decrease through beta decay. By examining the ratio of Carbon-14 to carbon-12 in organic remains, one can determine approximately how long ago that organism died.

A special thank you to Nobel Prize winner Willard Libby and his colleagues for developing this technique!