Radioactive Dating

Radioactive Dating Definition

To be able to understand radioactive dating, we need to review the basics of Radioactive Isotopes. Isotopes are atoms of the same element possessing the same number of protons and different numbers of neutrons in their nucleus.

Now, a radioactive isotope is an isotope that has an unstable nucleus. Because the nucleus of a radioactive isotope is not stable, it will spontaneously undergo radioactive (or nuclear) decay to turn into a daughter nuclide (also called a daughter isotope) containing a stable nucleus.

For example, the radioactive isotope of Nitrogen has an unstable nucleus, and spontaneously undergoes beta decay to turn into a stable oxygen nucleus. During beta decay, a type of radioactive decay, a beta (or electron) particle is emitted from an atomic nucleus.

$$ ^{16}_{7}\text{N }\longrightarrow \text{ }^{0}_{-1}\text{e + }^{16}_{8}\text{O} $$

Let's look at the definition of radioactive dating now.

In simpler terms, in radioactive dating, scientists count the number of parent Isotopes and daughter Isotopes formed from the nuclear decay to determine how many half-lives have passed and provide a suggestion of the age of an object.

For example, the radioactive isotope potassium-40 has a half-life of 1.3 billion years, meaning that it takes 1.3 billion years for one-half of the atoms of potassium-40 sample to decay into calcium-40 and argon-40.

$$ ^{40}_{19}\text{K }\longrightarrow \text{ }^{0}_{-1}\text{e + }^{40}_{20}\text{Ca} $$

$$ ^{40}_{19}\text{K } \text{ + }^{0}_{-1}\text{e } \longrightarrow ^{40}_{18}\text{Ar} $$

Radioactive Dating Techniques

Depending on the object that scientists are trying to study, different radioactive dating techniques can be used. For instance, potassium-40 can be used in the dating of rocks that are older than 100,000. But, why potassium-40? Well, it is because most rocks contain potassium!

The most common radioisotope used in radioactive dating techniques, however, is probably carbon-14. Carbon-14 is a radioactive isotope of Carbon that has a half-life of 5,720 years, and the reason it is very useful in the dating of fossils and some rocks is because it has a short half-life compared to other radioactive atoms. So, by using carbon-14, scientists can get a more accurate age. This technique is called radiocarbon (¹⁴C) dating, and it is useful to date objects back to 40,000 years.

The figure below shows stable and unstable isotopes of Carbon (carbon-12, and carbon-13), including the radioactive decay of the unstable isotope ¹⁴C into ¹⁴N. As time passes, carbon-14 decays into nitrogen-14, releasing lots of energy!

Other dating techniques involve using a uranium-lead (U-Pb) system for the dating of volcanic rocks, and rhenium-osmium (Re-Os) to date iron meteorites.

Radioactive Dating Method

Now that we know what radioactive isotopes are and how they can be used in radioactive dating, let's dig into the method used in the laboratory to determine the age of a rock.

Here, a mass spectrometer is used to measure the number of atoms of an element and determine the abundance of the parent and daughter isotopes (parent/daughter ratio) present in the rock. Then, the age of the rock is mathematically calculated using the half-life of the radioactive isotopes involved.

Radioactive Dating Formula

Once geologists determine the isotopic abundances of each parent/daughter elements using the mass spectrometer, the radioactive dating formula below can be used to find the age of the rock.

$$ t = \frac{1}{\lambda}\text{ln}(\frac{D}{P}) $$

Where:

• \( t \) is equal to the age of the rock or object
• \( \lambda \) is the decay constant
• \( D \) is the number of atoms of the daughter isotope
• \( P \) is the number of atoms of the parent isotope

Now, let's put this formula into practice! Let's say that you encountered a rock that contains 0.200 mg of Pb-206 for every 1.000 mg of U-238. Using laboratory methods, you found that the rock has 1.000 mg of U-206 and 1.231 mg of U-238.

Since the half-life for the decay of U-238 to Pb-206 is \( \text {4.5} \times \text {10}^{9} \) years and the decay constant is \( \text {1.5} \times \text {10}^{-10} \) years^-1 , how can we find the age of that rock? Let's find out!

From the problem, we know that U-238 is the parent isotope and Pb-206 is the daughter isotope formed from the decay of the nucleus of the parent isotope. Now, all we need to do it plug in the values into the radioactive dating formula.

$$ t = \frac{1}{1.5\times 10^{-10}}\text{ln}(\frac{1.000}{0.231}) = 1.7\times 10^{9}\text{ years} $$

Radioactive Dating Examples

Lastly, let's take a look at some examples involving radioactive dating. To predict how old the earth is, the ratio of Rb/Sr can be used. According to researchers, radioactive dating suggests that the earth is about \( \text {4.53} \times \text {10}^{9} \) years old!

Figure 4. Age of Earth, Isadora Santos - StudySmarter Originals.

Radioactive dating has also been used to determine the age of different mountains and volcanoes! For example, it was discovered that the age of a rock found at the top of the Grand Canyon yielded by a volcanic eruption was 1.143 billion years! However, radioactive dating is not always correct, and if contamination is present, it can yield an incorrect date result.

Now, I hope that you were able to understand radioactive dating a little better!