If you want to know how old someone or something is, you can generally rely on some combination of simply asking questions or Googling to arrive at an accurate answer. This applies to everything from the age of a classmate to the number of years the United States has existed as a sovereign nation (243 and counting as of 2019).

But what about the ages of objects of antiquity, from a newly discovered fossil to the very age of the Earth itself?

Sure, you can scour the Internet and learn rather quickly that the scientific consensus pins the age of of the planet at about **4.6 billion years**. But Google didn't invent this number; instead, human ingenuity and applied physics have provided it.

Specifically, a process called *radiometric dating* allows scientists to determine the ages of objects, including the ages of rocks, ranging from thousands of years old to billions of years old to a marvelous degree of accuracy.

This relies on a proven combination of basic mathematics and knowledge of the physical properties of different chemical elements.

## Radiometric Dating: How Does It Work?

To understand **radiometric dating techniques**, you first have to have an understanding of what is being measured, how the measurement is being made and the theoretical as well as practical limitations of the system of measurement being used.

As an analogy, say you find yourself wondering, "How warm (or cold) is it outside?" What you're actually looking for here is the temperature, which is fundamentally a description of how quickly molecules in the air are moving and colliding with one another, translated into a convenient number. You need a device to measure this activity (a thermometer, of which various kinds exist).

You also need to know when you can or cannot apply a particular type of device to the task at hand; for example, if you want to know how hot it is on the inside of an active wood stove, you probably understand that putting a household thermometer intended to measure body temperature inside the stove is not going to prove helpful.

Be aware also that for many centuries, most human "knowledge" of the age of rocks, formations such as the Grand Canyon, and everything else around you was predicated on the Genesis account of the Bible, which posits that the entire cosmos is perhaps 10,000 years old.

Modern geological methods have at times proven thorny in the face of such popular but quaint and scientifically unsupported notions.

## Why Use This Tool?

Radiometric dating takes advantage of the fact that the composition of certain minerals (rocks, fossils and other highly durable objects) changes over time. Specifically, the relative amounts of their constituent *elements* shift in a mathematically predictable way thanks to a phenomenon called *radioactive decay*.

This in turn relies on knowledge of *isotopes*, some of which are "radioactive" (that is, they spontaneously emit subatomic particles at a known rate).

**Isotopes** are different versions of the same element (e.g., carbon, uranium, potassium); they have the same number of *protons*, which is why the identity of the element does not change, but different numbers of *neutrons*.

- You are likely to encounter people and other sources that refer to radiometric dating methods generically as "radiocarbon dating " or just "carbon dating." This is no more accurate than referring to 5K, 10K and 100-mile running races as "marathons," and you'll learn why in a bit.

## The Concept of Half-Life

Some things in nature disappear at a more or less constant rate, regardless of how much there is to start with and how much remains. For example, certain drugs, including ethyl alcohol, are metabolized by the body at a fixed number of grams per hour (or whatever units are most convenient). If someone has the equivalent of five drinks in his system, the body takes five times as long to clear the alcohol as it would if he had one drink in his system.

Many substances, however, both biological and chemical, conform to a different mechanism: In a given time period, half of the substance will disappear in a fixed time no matter how much is present to start with. Such substances are said to have a *half-life*. Radioactive isotopes obey this principle, and they have wildly different decay rates.

The utility of this lies in being able to calculate with ease how much of a given element was present at the time it was formed based on how much is present at the time of measurement. This is because when radioactive elements first come into being, they are presumed to consist entirely of a single isotope.

As radioactive decay occurs over time, more and more of this most common isotope "decays" (i.e., is converted) into a different isotope or isotopes; these decay products are appropriately called *daughter isotopes*.

## An Ice Cream Definition of Half-Life

Imagine that you enjoy a certain kind of ice cream flavored with chocolate chips. You have a sneaky, but not especially clever, roommate who doesn't like the ice cream itself, but cannot resist picking out eating the chips – and in an effort to avoid detection, he replaces each one he consumes with a raisin.

He is afraid to do this with all of the chocolate chips, so instead, each day, he swipes half of the number of remaining chocolate chips and puts raisins in their place, never quite completing his diabolical transformation of your dessert, but getting closer and closer.

Say a second friend who is aware of this arrangement visits and notices that your carton of ice cream contains 70 raisins and 10 chocolate chips. She declares, "I guess you went shopping about three days ago." How does she know this?

It's simple: You must have started with a total of 80 chips, because you now have 70 + 10 = 80 total additives to your ice cream. Because your roommate eats half of the chips on any given day, and not a fixed number, the carton must have held 20 chips the day before, 40 the day before that, and 80 the day before that.

Calculations involving radioactive isotopes are more formal but follow the same basic principle: **If you know the half-life of the radioactive element and can measure how much of each isotope is present, you can figure out the age of the fossil, rock or other entity it comes from.**

## Key Equations in Radiometric Dating

Elements that have half-lives are said to obey a *first-order* decay process. They have what is known as a rate constant, usually denoted by k. The relationship between the number of atoms present at the start (N_{0}), the number present at the time of measurement N the elapsed time t, and the rate constant k can be written in two mathematically equivalent ways:

In addition, you may wish to know the *activity* A of a sample, typically measured in disintegrations per second or dps. This is expressed simply as:

A = kt

You don't need to know how these equations are derived, but you should be prepared to use them so solve problems involving radioactive isotopes.

## Uses of Radiometric Dating

Scientists interested in figuring out the age of a fossil or rock analyze a sample to determine the ratio of a given radioactive element's daughter isotope (or isotopes) to its parent isotope in that sample. Mathematically, from the above equations, this is N/N_{0}. With the element's decay rate, and hence its half-life, known in advance, calculating its age is straightforward.

The trick is knowing which of the various common radioactive isotopes to look for. This in turn depends in the approximate expected age of the object because radioactive elements decay at enormously different rates.

Also, not all objects to be dated will have each of the elements commonly used; you can only date items with a given dating technique if they include the needed compound or compounds.

## Examples of Radiometric Dating

**Uranium-lead (U-Pb) dating:** Radioactive uranium comes in two forms, uranium-238 and uranium-235. The number refers to the number of protons plus neutrons. Uranium's atomic number is 92, corresponding to its number of protons. which decay into lead-206 and lead-207 respectively.

The half-life of uranium-238 is 4.47 billion years, while that of uranium-235 is 704 million years. Because these differ by a factor of almost seven (recall that a billion is 1,000 times a million), it proves a "check" to make sure you're calculating the age of the rock or fossil properly, making this among the most precise radiometric dating methods.

The long half-lives make this dating technique suitable for especially old materials, from about 1 million to 4.5 billion years old.

U-Pb dating is complex because of the two isotopes in play, but this property is also what makes it so precise. The method is also technically challenging because lead can "leak" out of many types of rocks, sometimes making the calculations difficult or impossible.

U-Pb dating is often used to date igneous (volcanic) rocks, which can be hard to do because of the lack of fossils; metamorphic rocks; and very old rocks. All of these are hard to date with the other methods described here.

**Rubidium-strontium (Rb-Sr) dating:** Radioactive rubidium-87 decays into strontium-87 with a half -life of 48.8 billion years. Not surprisingly, Ru-Sr dating is used to date very old rocks (as old as the Earth, in fact, since the Earth is "only" around 4.6 billion years old).

Strontium exists in other stable (i.e., not prone to decay) isotopes, including strontium-86, -88 and -84, in stable amounts in other natural organisms, rocks and so on. But because rubidium-87 is abundant in the Earth's crust, the concentration of strontium-87 is much higher than that of the other isotopes of strontium.

Scientists can then compare the ratio of the strontium-87 to the total amount of stable strontium isotopes to calculate the level of decay that produces the detected concentration of strontium-87.

This technique is often used to date igneous rocks and very old rocks.

**Potassium-argon (K-Ar) dating:** The radioactive potassium isotope is K-40, which decays into both calcium (Ca) and argon (Ar) in a ratio of 88.8 percent calcium to 11.2 percent argon-40.

Argon is a noble gas, which means that it is nonreactive and would not be a part of the initial formation of any rocks or fossils. Any argon found in a rocks or fossils therefore has to be the result of this kind of radioactive decay.

The half-life of potassium is 1.25 billion years, making this technique useful for dating rock samples ranging from about 100,000 years ago (during the age of early humans) to around 4.3 billion years ago. Potassium is very abundant in the Earth, making it great for dating because it is found in some levels in most kinds of samples. It is good for dating igneous rocks (volcanic rocks).

**Carbon-14 (C-14) dating:** Carbon-14 enters organisms from the atmosphere. When the organism dies, no more of the carbon-14 isotope can enter the organism, and it will begin to decay starting at that point.

Carbon-14 decays into nitrogen-14 in the shortest half-life of all the methods (5,730 years), which makes it perfect for dating new or recent fossils. It is mostly only used for organic materials, that is, animal and plant fossils. **Carbon-14 cannot be used for samples older than 60,000 years old.**

At any given time, the tissues of living organisms all have the same ratio of carbon-12 to carbon-14. When an organism dies, as noted, it stops incorporating new carbon into its tissues, and so the subsequent decay of carbon-14 to nitrogen-14 alters the ratio of carbon-12 to carbon-14. By comparing the ratio of carbon-12 to carbon-14 in dead matter to the ratio when that organism was alive, scientists can estimate the date of the organism's death.

#### References

- The Nature Education Knowledge Project: Dating Rocks and Fossils Using Geologic Methods
- Tufts University: Radioactive Dating
- Georgia State University: HyperPhysics: Radioactive Dating
- Chemistry LibreTexts: The Kinetics of Radioactive Decay and Radiometric Dating
- Ptable: Dynamic Periodic Table of the Elements
- University of Regina: Carbon 14 Dating