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A technician of the U. Geological Survey uses a mass spectrometer to determine the proportions of neodymium isotopes contained in a sample of igneous rock. Cloth wrappings from a mummified bull Samples taken from a pyramid in Dashur, Egypt. This date agrees with the age of the pyramid as estimated from historical records.

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Unstable nuclei decay.

However, some nuclides decay faster than others. For example, radium and polonium, discovered by Marie and Pierre Curie, decay faster than uranium. That means they have shorter lifetimes, producing a greater rate of decay. Here we will explore half-life and activity, the quantitative terms for lifetime and rate of decay.

Why do we use the term like half-life rather than lifetime? The answer can be found by examining Figure The time in which half of the original of nuclei decay is defined as the half-lifet 1 2 t 1 2. After one half-life passes, half of the remaining nuclei will decay in the next half-life.

Then, half of that amount in turn decays in the following half-life. Nuclear decay is an example of a purely statistical process. A more precise definition of half-life is that each nucleus has a 50 percent chance of surviving for a time equal to one half-life. If an individual nucleus survives through that time, it still has a 50 percent chance of surviving through another half-life.

Even if it happens to survive hundreds of half-lives, it still has a 50 percent chance of surviving through one more. Therefore, the decay of a nucleus is like random coin flipping. The chance of he is 50 percent, no matter what has happened before. The probability concept aligns with the traditional definition of half-life.

Provided the of nuclei is reasonably large, half of the original nuclei should decay during one half-life period. The following equation gives the quantitative relationship between the original of nuclei present at time zero N O N O and the N N at a later time t. The decay constant can be found with the equation.

What do we mean when we say a source is highly radioactive? Generally, it means the of decays per unit time is very high.

We define activity R to be the rate of decay expressed in decays per unit time. In equation form, this is. The SI unit for activity is one decay per second and it is given the name becquerel Bq in honor of the discoverer of radioactivity. That is. Activity R is often expressed in other units, such as decays per minute or decays per year. The definition of the curie is. Radioactive dating or radiometric dating is a clever use of naturally occurring radioactivity. Its most familiar application is carbon dating. Carbon is an isotope of carbon that is produced when solar neutrinos strike 14 N 14 N particles within the atmosphere. Radioactive carbon has the same chemistry as stable carbon, and so it mixes into the biosphere, where it is consumed and becomes part of every living organism. Carbon has an abundance of 1. Over time, carbon will naturally decay back to 14 N 14 N with a half-life of 5, years note that this is an example of beta decay. When an organism dies, carbon exchange with the environment ceases, and 14 C 14 C is not replenished. Carbon dating can be used for biological tissues as old as 50 or 60 thousand years, but is most accurate for younger samples, since the abundance of 14 C 14 C nuclei in them is greater.

One of the most famous cases of carbon dating involves the Shroud of Turin, a long piece of fabric purported to be the burial shroud of Jesus see Figure This relic was first displayed in Turin in and was denounced as a fraud at that time by a French bishop. Its remarkable negative imprint of an apparently crucified body resembles the then-accepted image of Jesus.

As a result, the relic has been remained controversial throughout the centuries. Carbon dating was not performed on the shroud untilwhen the process had been refined to the point where only a small amount of material needed to be destroyed. Samples were tested at three independent laboratories, each being given four pieces of cloth, with only one unidentified piece from the shroud, to avoid prejudice.

All three laboratories found samples of the shroud contain 92 percent of the 14 C 14 C found in living tissues, allowing the shroud to be dated see Figure Carbon has a half-life of If 1 kg of carbon sample exists at the beginning of an hour, b how much material will remain at the end of the hour and c what will be the decay activity at that time? The decay constant is equivalent to the probability that a nucleus will decay each second.

As a result, the half-life will need to be converted to seconds. Another way of considering the decay constant is that a given carbon nuclei has a 0. The decay of carbon allows it to be used in positron emission topography PET scans; however, its As a result, one would expect the amount of sample remaining to be approximately one eighth of the original amount. The Calculate the age of the Shroud of Turin given that the amount of 14 C 14 C found in it is 92 percent of that in living tissue. Here, we assume that the decrease in 14 C 14 C is solely due to nuclear decay.

### Half life and radiometric dating

We enter that value into the equation to find t. Our calculation is only accurate to two digits, so that the year is rounded to That uncertainty is typical of carbon dating and is due to the small amount of 14 C in living tissues, the amount of material available, and experimental uncertainties reduced by having three independent measurements. There are other noncarbon forms of radioactive dating. Rocks, for example, can sometimes be dated based on the decay of U U. The decay series for U U ends with P b P bso the ratio of those nuclides in a rock can be used an indication of how long it has been since the rock solidified.

Knowledge of the U U half-life has shown, for example, that the oldest rocks on Earth solidified about 3. Learn about different types of radiometric dating, such as carbon dating. Understand how decay and half-life work to enable radiometric dating to work. Play a game that tests your ability to match the percentage of the dating element that remains to the age of the object. Learning Objectives Learning Objectives By the end of this section, you will be able to do the following: Explain radioactive half-life and its role in radiometric dating Calculate radioactive half-life and solve problems associated with radiometric dating Section Key Terms activity becquerel carbon dating decay constant half-life radioactive dating.

Tips For Success A more precise definition of half-life is that each nucleus has a 50 percent chance of surviving for a time equal to one half-life. Figure In one half-life t 1 2 t 1 2the decreases to half of its original value.

Half of what remains decays in the next half-life, and half of that in the next, and so on. This is exponential decay, as seen in the graph of the of nuclei present as a function of time. In equation form, this is Radiometric Dating Radiometric Dating Radioactive dating or radiometric dating is a clever use of naturally occurring radioactivity. The shroud first surfaced in the 14th century and was only recently carbon dated.

It has not been determined how the image was placed on the material.

### How old is earth, and how do we know?

Worked Example Carbon Decay Carbon has a half-life of Virtual Physics Radioactive Dating Game. Print Share. Related Items Resources No Resources. Videos No videos. Documents No Documents. Links No Links.

### Brooke

Radiometric dating, often called radioactive dating, is a technique used to determine the age of materials such as rocks.
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### Sindee

Radiometric dating calculates an age in years for geologic materials by measuring the presence of a short-life radioactive element, e.
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### Austin

Petrology Tulane University Prof.
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### Crista

But how is it dated?
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