When you are making popcorn, is there a way to be able to tell which kettle corn is going to pop first? Unfortunately, the answer to that question is no. Like popcorn, it is impossible to predict which or when an atom will decay, and once an atom undergoes radioactive decay, it cannot be converted back into what it was before the decay took place. In some cases, these atoms deemed radioactive can be used in radioactive dating, assisting geologists and paleontologists in determining the age of certain things that are found around us.

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So, let's jump right into the world of radioactive dating.

• Then, we will look at techniques and methods surrounding radioactive dating.
• Next, we will learn the radioactive dating formula and also look at some examples.

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.

The process in which the nucleus of a radioactive isotope (the parent isotope) undergoes decay to become a stable daughter nuclide (also referred to as a daughter isotope) is called radioactive decay.

A Daughter Nuclide results from the radioactive decay of a parent isotope. The daughter nuclide (daughter isotope) will decay into a different atom relative to the parent isotope.

A Nuclide is a particular instance of an atom of an atomic nucleus, for example, $$^{16}_{8}\text{O}$$, is a particular nucleus of oxygen.

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.

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

Looking for an in-depth explanation of radioisotopes or on the different types of nuclear decay? Check out "Radioactive Isotopes" and "Balancing Nuclear Equations"!

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

Radioactive dating involves using the half-life of nuclides to determine the age of a fossil or object.

• The half-life of a radioactive isotope is referred to as the time taken for 50% of its nucleus to decay.

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.

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

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

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.

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.

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.

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

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!

## Radioactive Dating - Key takeaways

• The process in which the nucleus of a radioactive isotope (the parent isotope) undergoes decay to a become a stable daughter isotope is called radioactive decay.
• Radioactive dating involves using the half-life of nuclides to determine the age of a fossil or object.
• The half-life of a radioactive isotope is referred to as the time taken for 50% of its nucleus to decay.

## References

1. Zumdahl, S. S., Zumdahl, S. A., & Decoste, D. J. (2019). Chemistry. Cengage Learning Asia Pte Ltd.
2. Theodore Lawrence Brown, Eugene, H., Bursten, B. E., Murphy, C. J., Woodward, P. M., Stoltzfus, M. W., & Lufaso, M. W. (2018). Chemistry : the central science (14th ed.). Pearson.
3. Graham, I. (2020, September 30). Radioactive dating. The Australian Museum. https://australian.museum/learn/minerals/shaping-earth/radioactive-dating/

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what are the 3 types of radioactive dating?

The three common types of radioactive dating include the carbon-14 method, the U-Pb method and the Rb-Sr method.

Radioactive dating is a technique that involves of use of the half-life of nuclides to determine the age of a fossil or object.

Radioactive dating, helps geologists and paleontologists to determine the age of objects.

How do radioactive dating techniques work?

Radioactive dating techniques work by measuring the abundance of the parent and daughter isotopes, and using the half-life of the parent isotope to find out the age of an object.

How do you solve radioactive dating problems?

To solve dating problems, we can use the formula for radioactive dating: $$t = \frac{1}{\lambda}\text{ln}(\frac{D}{P})$$.

## Test your knowledge with multiple choice flashcards

The process in which the nucleus of a ______ (the parent isotope) undergoes decay to a become a stable daughter isotope is called radioactive decay.

The radioactive isotope of nitrogen has an unstable nucleus, and spontaneously undergoes beta decay to turn into a stable  _____ nucleus.

_____  involves using the half-life of nuclides to determine the age of a fossil or object.

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