Radioactive Decay Notes & Assignment
Introduction
Unstable nuclei of radioisotopes become stable by emitting charged particles and energy. This process is called radioactive decay. It is a nuclear, as opposed to chemical, reaction, in which one element changes into another.
Types of Radioactive Decay
There are three types of radioactive decay: alpha, beta, and gamma decay. In all three types, nuclei emit radiation, but the nature of that radiation differs from one type of decay to another. You can watch a video about the three types at this URL: http://www.youtube.com/watch?v=3koOwozY4oc (17:02).
Alpha decay occurs when an unstable nucleus emits an alpha particle and energy. The diagram in Figure below represents alpha decay. An alpha particle contains two protons and two neutrons, giving it a charge of +2. A helium nucleus has two protons and two neutrons, so an alpha particle is represented in nuclear equations by the symbol 42He. The superscript 4 is the mass number (2 protons + 2 neutrons). The subscript 2 is the charge of the particle as well as the number of protons.
Alpha decay results in the loss of two protons and two neutrons from a nucleus.
An example of alpha decay is the decay of Uranium-238 to Thorium-234. In this reaction, Uranium loses two protons and two neutrons to become the element Thorium. The reaction can be represented by this equation:
238 92U→234 90Th + 42He + Energy
If you count the number of protons and neutrons on each side of this equation, you’ll see that the numbers are the same on both sides of the arrow. This means that the equation is balanced. The Thorium-234 produced in this reaction is unstable, so it will undergo radioactive decay as well. The alpha particle (42He) produced in the reaction can pick up two electrons to form the element helium. This is how most of Earth’s helium formed.
Problem Solving
Problem: Fill in the missing subscript and superscript to balance this nuclear equation: 208 84 Po→ ??Pb + 42 He + Energy
Solution: The subscript is 82, and the superscript is 204.
You Try It!
Problem: Fill in the missing subscript and superscript to balance this nuclear equation: 222 ?Ra→ ? 86 Rn + 42 He + Energy
Beta decay occurs when an unstable nucleus emits a beta particle and energy. A beta particle is an electron. It has a charge of -1. In nuclear equations, a beta particle is represented by the symbol 0−1e. The subscript -1 represents the particle’s charge, and the superscript 0 shows that the particle has virtually no mass. Nuclei contain only protons and neutrons, so how can a nucleus emit an electron? A neutron first breaks down into a proton and an electron (see Figure below). Then the electron is emitted from the nucleus, while the proton stays inside the nucleus. The proton increases the atomic number by one, thus changing one element into another.
In beta decay, an electron and a proton form from a neutron (another unusual particle, called an antineutrino, is also produced). Only the electron is emitted from the nucleus. How does this change the atomic number and atomic mass of the atom?
An example of beta decay is the decay of Thorium-234 to Protactinium-234. In this reaction, Thorium loses a neutron and gains a proton to become Protactinium. The reaction can be represented by this equation:
234 90 Th → 234 91Pa + 0−1e + Energy
The protactinium-234 produced in this reaction is radioactive and decays to another element. The electron produced in the reaction (plus another electron) can combine with an alpha particle to form helium.
Problem Solving
Problem: Fill in the missing subscript and superscript in this nuclear equation: 131 53I→ ?? Xe + 0−1e + Energy
Solution: The subscript is 54, and the superscript is 131.
You Try It!
Problem: Fill in the missing subscript and superscript in this nuclear equation: 14 ?C→ ?7N+ 0−1e + Energy
In alpha and beta decay, both particles and energy are emitted. In gamma decay, only energy is emitted. Gamma decay occurs when an unstable nucleus gives off gamma rays. Gamma rays, like rays of visible light and X-rays, are waves of energy that travel through space at the speed of light. Gamma rays have the greatest amount of energy of all such waves. By itself, gamma decay doesn’t cause one element to change into another, but it is released in nuclear reactions that do. Some of the energy released in alpha and beta decay is in the form of gamma rays. You can learn more about gamma radiation at this URL: http://www.youtube.com/watch?v=okyynBaSOtA (2:45).
The different types of radiation vary in how far they are able to travel and what they can penetrate (see Figure below and the URL below).
http://www.youtube.com/watch?v=ec8iomUS34U (0:30)
● Alpha particles can travel only a few centimeters through air. They cannot pass through a sheet of paper or thin layer of clothing. They may burn the skin but cannot penetrate tissues beneath the skin.
● Beta particles can travel up to a meter through air. They can pass through paper and cloth but not through a sheet of aluminum. They can penetrate and damage tissues beneath the skin.
● Gamma rays can travel thousands of meters through air. They can pass through a sheet of aluminum as well as paper and cloth. They can be stopped only by several centimeters of lead or several meters of concrete. They can penetrate and damage organs deep inside the body.
It’s easy to stop alpha particles and even beta particles. However, it’s very difficult to stop gamma rays.
Rate of Radioactive Decay
A radioactive isotope decays at a certain constant rate. The rate is measured in a unit called the half-life. This is the length of time it takes for half of a given amount of the isotope to decay. The concept of half-life is illustrated in Figure below for the beta decay of phosphorus-32 to sulfur-32. The half-life of this radioisotope is 14 days. After 14 days, half of the original amount of phosphorus-32 has decayed. After another 14 days, half of the remaining amount (or one-quarter of the original amount) has decayed, and so on.
This diagram models the rate of decay of phosphorus-32 to sulfur-32.
Different radioactive isotopes vary greatly in their rate of decay. As you can see from the examples in Table below, the half-life of a radioisotope can be as short as a split second or as long as several billion years.
Some radioisotopes decay much more quickly than others.
Isotope |
Half-life |
Uranium-238 |
4.47 billion years |
Potassium-40 |
1.28 billion years |
Carbon-14 |
5,730 years |
Hydrogen-3 |
12.3 years |
Radon-222 |
3.82 days |
Polonium-214 |
0.00016 seconds |
Problem Solving
Problem: If you had a gram of carbon-14, how many years would it take for radioactive decay to reduce it to one-quarter of a gram?
Solution: One gram would decay to one-quarter of a gram in 2 half-lives (12×12=14), or 2 × 5,730 years = 11,460 years.
You Try It!
Problem: What fraction of a given amount of hydrogen-3 would be left after 36.9 years of decay?
Radioactive Dating
Radioactive isotopes can be used to estimate the ages of fossils and rocks. The method is called radioactive dating. Carbon-14 dating is an example of radioactive dating. It is illustrated in the video at this URL: http://www.youtube.com/watch?v=udkQwW6aLik (11:00).
Carbon-14 forms naturally in Earth’s atmosphere when cosmic rays strike atoms of nitrogen-14. Living things take in and use carbon-14, just as they do carbon-12. The carbon-14 in living things gradually decays to nitrogen-14. However, it is constantly replaced because living things keep taking in carbon-14. As a result, there is a fixed ratio of carbon-14 to carbon-12 in organisms as long as they are alive. This is illustrated in the top part of Figure below.
After organisms die, the carbon-14 they already contain continues to decay, but it is no longer replaced (see bottom part of Figure below). Therefore, the carbon-14 in a dead organism constantly declines at a fixed rate equal to the half-life of carbon-14. Half of the remaining carbon-14 decays every 5,730 years. If you measure how much carbon-14 is left in a fossil, you can determine how many half-lives (and how many years) have passed since the organism died.
After organisms die, the carbon-14 they contain is lost at a constant rate.
Carbon-14 has a relatively short half-life (see Table above). After about 50,000 years, too little carbon-14 is left in a fossil to be measured. Therefore, carbon-14 dating can only be used to date fossils that are less than 50,000 years old. Radioisotopes with a longer half-life, such as potassium-40, must be used to date older fossils and rocks.