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Difficulty Level: At Grade Created by: CK-12

## Lesson Objectives

The student will:

• compare qualitatively the ionizing and penetration power of \begin{align*} \alpha\end{align*}, \begin{align*} \beta\end{align*}, and \begin{align*} \gamma\end{align*} particles.
• calculate the amount of radioactive material that will remain after an integral number of half-lives.
• describe how carbon-14 is used to determine the age of carbon containing objects.

## Vocabulary

• half-life
• ionizing power
• penetration power

## Introduction

All of us are subjected to a certain amount of ionizing radiation every day. This radiation is called background radiation and comes from a variety of natural and artificial radiation sources. Approximately 82% of background radiation comes from natural sources. These include 1) sources in the earth and naturally occurring radioactive elements which are incorporated in building materials and in the human body, 2) sources from space in the form of cosmic rays, and 3) sources in the atmosphere, such as radioactive radon gas released from the earth and radioactive atoms like carbon-14 produced in the atmosphere by bombardment from high-energy cosmic rays.

Approximately 15% of background radiation comes from medical X-rays and nuclear medicine. The remaining 3% of background radiation comes from man-made sources such as: smoke detectors, luminous dials and signs, radioactive contamination due to historical nuclear weapons testing, normal operation of facilities used for nuclear power and scientific research, emissions from burning fossil fuels (primarily coal-burning power plants without ash-capture facilities), and emissions from the improper disposal of radioactive materials used in nuclear medicine.

It is recommended that individuals limit exposure to ionizing radiation as much as possible. To this goal, the medical profession has significantly reduced the number of X-rays recommended: skin tests for tuberculosis are recommended over X-rays, and most dentists recommend dental X-rays every other check-up instead of every check-up.

## The Ionizing and Penetration Power of Radiation

With all the radiation from natural and man-made sources, we should be quite reasonably concerned about how all the radiation might affect our health. The damage to living systems done by radioactive emissions is when the particles or rays strike and alter tissue, cells, or molecules. These interactions can alter molecular structure and function, causing cells to no longer carry out their proper function and molecules, such as DNA, to no longer carry the appropriate information.

Large amounts of radiation are very dangerous, even deadly. The ability of radiation to damage molecules is analyzed in terms of what is called ionizing power. When a radiation particle interacts with atoms, the interaction can cause the atom to lose electrons and thus become ionized. The ionizing power of the radiation reflects the likelihood that damage will occur by such an interaction. Much of the threat from radiation is involved with the ease or difficulty of protecting oneself from the particles. The ability of each type of radiation to pass through matter is expressed in terms of penetration power. The more material the radiation can pass through, the greater the penetration power and the more dangerous they are.

Comparing the three common types of ionizing radiation, alpha particles have the greatest mass. Alpha particles have approximately four times the mass of a proton or neutron and approximately 8,000 times the mass of a beta particle. Because of the large mass of the alpha particle, it has the highest ionizing power and the greatest ability to damage tissue. The large size of alpha particles, however, makes them less able to penetrate matter. They collide with molecules very quickly when striking matter, add two electrons, and become a harmless helium atom. Alpha particles have the least penetration power and can be stopped by a thick sheet of paper. They are also stopped by the outer layer of dead skin on people. This may seem to be enough to remove the threat from alpha particles, but this is only true if the radiation comes from external sources. In a situation like a nuclear explosion or some sort of nuclear accident where radioactive emitters are spread around in the environment, the emitters can be inhaled or taken in with food or water. Once the alpha emitter is inside you, you will have no protection at all.

Beta particles are much smaller than alpha particles. Consequently, they have much less ionizing power (less ability to damage tissue), but their small size gives them much greater penetration power. Most resources say that beta particles can be stopped by a one-quarter inch thick sheet of aluminum. Once again, however, the greatest danger occurs when the beta emitting source gets inside of you.

Gamma rays are energy that has no mass or charge. Gamma rays have tremendous penetration power and require several inches of dense material (like lead) to shield them. Gamma rays may pass all the way through a human body without striking anything. They are considered to have the least ionizing power and the greatest penetration power.

When researching thicknesses and materials required to stop various types of radiation, different estimates are encountered. There are apparently two reasons for this: 1) some estimates are based on stopping \begin{align*}95\%\end{align*} of beta particles while other estimates are based on stopping \begin{align*}99\%\end{align*} of beta particles, and 2) different beta particles emitted during nuclear reactions may have very different energies – some very high energy beta particles may not be stopped by the normal barrier.

For a lecture about types of nuclear decay including the ionizing and penetration power of the three major types of radioactive emissions (11e), see http://www.youtube.com/watch?v=aEBGE1Nm7vc (7:57).

## Definition of Half-Life

During natural radioactive decay, not all atoms of an element are instantaneously changed to atoms of another element. The decay process takes time, and there is value in being able to express the rate at which a process occurs. In chemical reactions as well as radioactive decay, a useful concept is the half-life, which is the time required for half of the starting material to be consumed. Half-lives can be calculated from measurements on the change in mass of a nucleus and the time it takes to occur. For a particular group of radioactive nuclei, it is not possible to know which nuclei will disintegrate or when they will disintegrate. The only thing we know is that in the time of that substance’s half-life, half of the original nuclei will disintegrate.

## Selected Half-Lives

The half-lives of many radioactive isotopes have been determined and found to range from extremely long half-lives of 10 billion years to extremely short half-lives of fractions of a second (Table below).

Table of Selected Half-Lives
Element Mass Number Half-Life Element Mass Number Half-Life
Uranium \begin{align*}238\end{align*} \begin{align*}4.5\end{align*} billion years Californium \begin{align*}251\end{align*} \begin{align*}800\end{align*} years
Neptunium \begin{align*}240\end{align*} \begin{align*}1\end{align*} hour Nobelium \begin{align*}254\end{align*} \begin{align*}3\end{align*} seconds
Plutonium \begin{align*}243\end{align*} \begin{align*}5\end{align*} hours Carbon \begin{align*}14\end{align*} \begin{align*}5,770\end{align*} years
Americium \begin{align*}246\end{align*} \begin{align*}25\end{align*} minutes Carbon \begin{align*}16\end{align*} \begin{align*}0.74\end{align*} seconds

The quantity of radioactive nuclei at any given time will decrease to half as much in one half-life. For example, if there were \begin{align*}100 \ \mathrm{g}\end{align*} of \begin{align*}\mathrm{Cf}-251\end{align*} in a sample at some time, after \begin{align*}800\end{align*} years, there would be \begin{align*}50 \ \mathrm{g}\end{align*} of \begin{align*}\mathrm{Cf}-251\end{align*} remaining. After another \begin{align*}800\end{align*} years, there would only be \begin{align*}25 \ \mathrm{g}\end{align*} remaining.

Half-life is defined and explained in the first video (11f) http://www.youtube.com/watch?v=9REPnibO4IQ (12:31).

The second video is an introduction to exponential decay (11f, I&E 1e) http://www.youtube.com/watch?v=HTDop6eEsaA (9:19).

An ingenious application of half-life studies established a new science of determining ages of materials by half-life calculations. For geological dating, the decay of U-238 can be used. The half-life of U-238 is \begin{align*}4.5 \times 10^9\end{align*} years. The end product of the decay of U-238 is Pb-206. After one half-life, a \begin{align*}1.00\end{align*} gram sample of uranium will have decayed to \begin{align*}0.50\end{align*} grams of U-238 and \begin{align*}0.43 \ \mathrm{grams}\end{align*} of Pb-206. By comparing the amount of U-238 to the amount of Pb-206 in a sample of uranium mineral, the age of the mineral can be estimated. Present day estimates for the age of the Earth’s crust from this method is at least 4 billion years.

Organic material is radioactively dated using the long-lived carbon-14. This method of determining the age of organic material was given the name radiocarbon dating. The carbon dioxide consumed by living systems contains a certain concentration of \begin{align*}^{14}\mathrm{CO}_2\end{align*}. When the organism dies, the acquisition of carbon-14 stops, but the decay of the C-14 in the body continues. As time goes by, the ratio of C-14 to C-12 decreases at a rate determined by the half-life of C-14. Using half-life equations, the time since the organism died can be calculated. These procedures have been used to determine the age of organic artifacts and determine, for instance, whether art works are real or fake.

## Lesson Summary

• 82% of background radiation comes from natural sources.
• Approximately 15% of background radiation comes from medical X-rays and nuclear medicine. The remaining 3% of background radiation comes from man-made sources.
• Of the three common nuclear emissions, alpha particles produce the greatest damage to cells and molecules but are the least penetrating. Gamma rays are the most penetrating but generate the least damage.
• C-14 dating procedures have been used to determine the age of organic artifacts.

The website below displays a map that shows the amount of environmental radiation across the United States.

## Review Questions

1. Which of the three common emissions from radioactive sources requires the heaviest shielding?
2. The half-life of radium\begin{align*}-226\end{align*} is about \begin{align*}1600\;\mathrm{years.}\end{align*} How many grams of a \begin{align*}2.00\;\mathrm{gram}\end{align*} sample will remain after \begin{align*}4800\;\mathrm{years?}\end{align*}
3. Sodium\begin{align*}-24\end{align*} has a half-life of about \begin{align*}15\;\mathrm{hours.}\end{align*} How much of an \begin{align*}16.0\;\mathrm{grams}\end{align*} sample of sodium-\begin{align*}24\end{align*} will remain after \begin{align*}60.0\;\mathrm{hours?}\end{align*}
4. A radioactive isotope decayed from \begin{align*}24.0\;\mathrm{grams}\end{align*} to \begin{align*}0.75\;\mathrm{grams}\end{align*} in \begin{align*}40.0\;\mathrm{years.}\end{align*} What is the half-life of the isotope?
5. What nuclide is commonly used in the dating of organic artifacts?
6. Why does an ancient wood artifact contain less carbon\begin{align*}-14\end{align*} than a piece of lumber sold today?
7. The half-life of \begin{align*}\mathrm{C}-14\end{align*} is about \begin{align*}5,700 \ \mathrm{years.}\end{align*} An organic relic is found to contain \begin{align*}\mathrm{C}-14\end{align*} and \begin{align*}\mathrm{C}-12\end{align*} in a ratio that is about one-eighth as great as the ratio in the atmosphere. What is the approximate age of the relic?
8. Even though gamma rays are much more penetrating than alpha particles, it is the alpha particles that are more likely to cause damage to an organism. Explain why this is true.
9. The radioactive isotope calcium\begin{align*}-47\end{align*} has been used in the study of bone metabolism; radioactive iron\begin{align*}-59\end{align*} has been used in the study of red blood cell function; iodine\begin{align*}-131\end{align*} has been used in both diagnosis and treatment of thyroid problems. Suggest a reason why these particular elements were chosen for use with the particular body function.

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