The Essentials - Old Man River’s Got Nothin’ on You Earth (Part 2.2)

Clocks in the rocks

Carbon 14 (C14) predictably decays to Nitrogen 14 (N14) at a rate of half of the total sample every 5,000 years (OK fact checkers not exactly 5,000 but it will make the math easier in a few sentences. You should also brace yourself because I’ll use some even more ridiculously simplistic numbers in the next paragraph). This decay rate is called the half life. As you savvy readers may have realized the half life can be used to estimate the time since the rock was formed.  If you’re not so savvy, (Don’t worry if you’re not. I’m still trying to wrap my mind around the math of it) When I’m feeling underwhelmed by my understanding I find it helpful to work through a scenario. So let’s do this thing.

1) Let’s say a rock has 512 C14 and 512 N14.  From this ratio, and the known 5,000 year half life of C14, we can deduce that the rock started with 1024 (512 +512) C14 and is 5,000 years old.  In other words half of the C14 is gone so we know one half life has passed.

2) Now let’s say the rock has 256 C14 and 768 N14. From this ratio, and the known half life of C14, we can deduce that the rock started with 1024 C14 and is 10,000 years old. In the first 5,000 years the original 1024 C14 were halved to 512 leaving 512 N14.  In the second 5000 years the remaining 512 C14 was cut in half to 256 C14 and the 256 newly created N14 were added to the original 512 from the first 5,000 years for a total of 768 N14.

3) 5,000 years later (15,000 years in total) there will be 128 C14 and 896 N14. This C14 halving and N14 accumulating will continue until all of the C14 is gone (or there is not enough to discernibly measure).  The chart below carries this logic through to the end of its usefulness. After 50,000 years there isn’t enough C14 to measure, or be halved, so at this point we can only say that the rock is older than 50,000 years.

Total Age	Total Remaining C14	Accumulated N14
>50000	<1	>1023
50000	1	1023
45000	2	1022
40000	4	1020
35000	8	1016
30000	16	1008
25000	32	992
20000	64	960
15000	128	896
10000	256	768
5000	512	512
0 (The rock is formed)	1024	0

While this was a simplistic example, and the C14 numbers should be a lot bigger, it does show how the half life of an isotope like C14 can be used to estimate the age of a rock. In fact the usefulness of C14 for dating does have an upper limit of around 50,000 years.  If C14 was the only available isotope, the upper reliable limit of our Earth age estimation would be 50,000 years.  This wouldn’t mean that the Earth could only be 50,000 but rather we could only reliably say the Earth is older than 50,000 years old. THere may be a term for the case when the effectiveness for dating sails over and beyond the horizon of physical observability but I don't know it.  I think I'll call it "The at least hypothesis."

Fortunately there are many types of isotopes with a wide range of half lives, some very short and some very long. By using a range of isotopes with half lives of millions and billions of years scientists have estimated the age of the Earth at about 4.5 billion years.