Principles of Radiometric (Isotopic) Dating

The details of radiometric (also called isotopic) dating are quite complex!  Entire books are written on the subject and entire scientific journals are devoted to this discipline.

But the bare-bones idea is pretty straightforward.  And that’s what we need introductory students to learn.  Consider these four simple steps to understanding radiometric dating.

1st,
Elements are defined by their atomic number, which is just the number of protons in their atomic nucleus.
Remember, the nucleus of an atom consists of protons and neutrons; with a relatively enormous shell of electrical energy surrounding the tiny, but massive, nucleus that contains the electrons.  Protons and neutrons weigh nearly 2000 times that of electrons.
If an atom contains 79 protons, it’s gold.  If an atom contains 8 protons, it’s oxygen.
Each element has a very specific atomic number, i.e. number of protons in its nucleus.

2nd,
Elements can have varying amounts of neutrons in the nucleus, and therefore we say that each element has a variety of isotopes.
For example, Hydrogen by definition has only one proton;  but our little hydrogen atom can have either zero neturons (“normal hydrogen”), or 1 neturon (called “deuterium hydrogen”– occurs naturally) or 2 neutrons (called “tritium hydrogen”– not naturally occurring but can be produced in a nuclear reactor).  Each of these variants (all with 1 proton) is specific isotope of hydrogen.
Another Example:  Above, we noted that oxygen contains 8 protons– and it normally contains 8 neutrons (atomic mass 16), but it can also have 9 or 10 neutrons (atomic masses of 17 and 18 respectively). Each of these variants is called an isotope of oxygen.

3rd,
Some isotopes DECAY over time.  Which means that their internal nuclear structure and content CHANGES.
K-40 (a kind of potassium isotope with 19 protons and 21 neutrons), DECAYS over time to Ca-40 and Ar-40.
U-238 (a kind of uranium isotope with 92 protons and 146 neutrons), DECAYS over time to a variety of products, and eventually to Pb-206.
The starting isotope (K-40 or U-238, for example) is called the PARENT ISOTOPE, and the end product (Ar-40 or Pb-206, for example) is called the DAUGHTER ISOTOPE.

The details here are not crucial, but notice that Parent Decay can occur in a variety of mechanisms, e.g. —

• Losing an alpha particle, or helium nucleus;
• Gaining or losing an electron via modification of neutrons and protons (within the nucleus, and not in the electron shell);
• Emission of high energy light (electromagnetic radiation) called gamma radiation.

from,
https://ib.bioninja.com.au/standard-level/topic-5-evolution-and-biodi/51-evidence-for-evolution/radioactive-dating.html

4th,
Here’s the cool part–
If a rock contains a lot of PARENT (say K-40) and very little DAUGHTER (say Ar-40), then it has not been sitting around for long.  The parent has NOT decayed much, and the rock is YOUNG.
If a rock contains very little parent and quite a bit of daughter, then the rock is probably quite old.
Since we know the RATE at which these radioactive isotopes decay, it’s possible to calibrate the whole thing and determine quantitative rock ages!

Half Life Concept

Decay of radioactive isotopes is a statistical process.  All decay occurs via a statistical rule called half-life.
If a lot of an isotope is present, then its abundance decreases rapidly.  Look at the standard curves below for parent decay and daughter accrual, below.
This is the pattern for all radioactive decays schemes.
The blue line (showing decrease of parent) is rather steep initially, then it shallows!

Half-life simply refers to the amount of time that it takes for a GIVEN amount of a radioactive parent to decay by 1/2 or 50%.
Notice that as the parent decays, the daughter abundance grows!

homepages.uc.edu

Since this is the fundamental law for radioactive decay, no matter what pair (Isotopes of Nd decays to Sm, K decays to Ar, Rb to Sr, U to Pb, etc etc),
if a rock starts with a hundred atoms (or a hundred pounds or a hundred “bushels”) of Parent, then–

• after 1 half life, the Parent is down to 50 (atoms or pounds or whatever), and the daughter grows from zero to 50.
• After another half life, the Parent is down to 25, and the daughter grows to 75.

So, after 1 half life the D/P ratio is 1:1,, and after 2 half lives it is 3:1.
After 3 half lives, it’s a ratio of 87.5:12.5 (or 7:1).
If you KNOW the D/P ratio in a rock, AND if you know the half-life, then you know how many half lives have transpired and you know the AGE of the rock.

Below, from Steven Earle, Physical Geology– half lives of various parent/daughter radioactive systems.
Ga means giga-anum, and is the same as saying “billion years.”

If only it was so easy!

Mass Spectrometer, Used to measure isotope and isotopic ratios.

In practice, radiometric dating is challenging.  
But the challenges can be overcome, and using modern equipment that is capable of weighing individual atoms, and identifying isotopes, it can be exceedingly accurate and (most importantly) reproducible and commensurate with other geologic observations.

The challenges come from things like–
1) How do you account for a rock already containing some daughter product when it forms?  (Isochron techniques provided the solution.)
2) What if a rock is leaky, and over time it has lost some of the daughter product?
(Various tests can be devised to check for this.)

Carbon Dating Note

CONTRARY TO POPULAR CONCEPTION– Carbon dating, based on the decay of C-14 to N-14 is not something that is used on rocks.  It requires that the material have “interacted” with the atmosphere through respiration or photosynthesis.
This is because C-14, as you can see from the table above, has a very short half life.  Over the age of the earth, and most rocks, any and all C-14 would be virtually gone!  (Say the half life is about 6000yrs— so after 6ky only 50 atoms of an original 100 atoms would be left;  after 12000yrs only 25 atoms left; after 18000yrs only 12.5 atoms left; etc etc,, such that after just a few hundred thousand years there would be virtually no C-14 left!)
Watch the video below,,
You’ll learn that C-14 is being continuously generated in earth’s upper atmosphere, then circulated in lower atmosphere, and then incorporated into LIVING things.  After those living things die, their C-14 rapidly decays away!

Here is an interesting interactive tool for investigating how radiometric dating works.  It requires that your computer has JAVA, and is best (at least on a PC) to use browsers such as Firefox or Chrome, or anything other than Edge.

Dating Game

https://phet.colorado.edu/en/simulation/legacy/radioactive-dating-game