Scope, Sequence, and Coordination

A Framework for High School Science Education

Based on the National Science Education Standards

Radioactivity, Time and Age

Earth’s Internal Energy Sources: Radioactivity and Gravitational Potential Energy
Two primary sources of internal energy are the decay of radioactive isotopes and the gravitational energy from the earth’s original formation.

Further Description:

When Becquerel (1896) accidentally placed a uranium sample on a photographic plate, he found the plate to be partially exposed. This startling discovery led to the discovery of radioactivity. Materials that are radioactive contain atoms whose nuclei split apart, giving off energy and charged particles. As the nuclei break apart, the resulting radiation is absorbed by matter to produce heat. In many cases the radiation is in the form of extremely short-wavelength gamma radiation, and also there are often particles, alpha (helium nuclei) or beta (electrons), that can have considerable energies. These radiations and particles interact with other particles, transferring energy that ultimately becomes heat in the material that has absorbed the radiation. This is the form of heat that warms the interior of the earth. This radioactive decay produces energy, and a more stable element is formed.

Although Earth’s average heat from radioactivity and the original gravitational sources is extremely small on the average compared with energy from the sun, there are "hot spots" around Earth. (Gravitational heat is energy released when masses aggregate, converting their original potential energy due to their separation into heat energy.) The original gravitational heat, along with the production of heat by radioactivity in the earth, is still very substantial, so much so that at depths of 30--50 km, the temperature is more than 500 oC. It is especially interesting that heat flow decreases with the age of ocean floors or continental areas. This decrease is connected to fundamental properties of radioactivityChalf-life and mean lifetime, which allow us to date these areas.

Certain minerals contain radioactive elements, and the rates at which these elements decay can be determined and used to date events in Earth’s history. Radioactive decay is a measure of geological absolute time. Boltwood, an American chemist, first devised a method of using radioactivity to determine the age of a substance. He found that you could calculate the age if you compared the amount of the parent material (such as uranium) contained in a sample with the amount of the decay product (in the case of uranium the stable product is lead-206). For ancient rocks, only four radioactive isotopes are helpful. They are uranium-238, uranium-235, potassium-40, and rubidium-87. Most of these elements occur in igneous rocks. Uranium-238 is the most commonly used radioactive isotope in this dating process. Its half-life is 4.5 billion years.

Carbon-14, with a half-life of 5,730 years, allows us to date rocks formed more recently and to date organic material. This radioactive isotope is produced in the upper atmosphere and mixes with regular carbon dioxide in the atmosphere. The ratio of carbon-14 to regular carbon is very constant. Living organisms continuously exchange carbon atoms with their surroundings, so that the ratio is constant in living matter as long as it is alive. As soon as the living matter dies, it no longer replaces the carbon and the ratio begins to decrease as radioactive decay of carbon-14 occurs. The amount of activity then indicates the date when the living matter died. Similarly, carbon-14 atoms in certain rocks will decay. Thus, the ratio of radioactive to regular carbon dioxide molecules gives a measure of age of the sample.

The decay products of uranium-238 include eight alpha particles, beta decay, and gamma decay. An alpha particle is composed of two protons and two neutrons. A beta particle is an electron that is emitted from the neutrons in the nucleus. Uranium-238 decays through a chain of other transformations, ultimately producing lead-206 and eight helium atoms. Since helium gas is produced, one method of dating samples is to measure the amount of helium gas trapped in a rock with U-238 and lead. Since the half-life of uranium is 4.5 billion years, a gram of U-238 would produce so few decays per year that the heat produced would be only about 3.2 joules of energy per year per gram of U-238. This seems as though it is a very small amount of heat; however, even at 60 mW per square meter, heat coming from the earth’s interior amounts to about 9 H 1020 J/year. If all of this heat were produced by U-238 decay, it would require that only 0.00046% of the earth’s mass be U-238, perhaps not an unreasonable number. A study of radioactive decay provides some clues to the structure of the earth’s interior. In addition, it provides clues to the earth’s formation.

Residual gravitational energy is very difficult to study. It is largely associated with the molten inner core of the earth, which cannot be a source of additional heat. Earth matter that is carried to the surface brings much of this heat, and in that sense the original sourceCgravitational potential energyCis being observed.

Concepts Needed:

Grade 9

Radioactivity (as a macroscopic phenomenon), half-life, mean lifetime, density, mantle, crust, core

Grade 10

Radioactivity, radioactive isotopes, half-life, radioactive decay, nuclear reactions

Grade 11

Isotopes, radioactive, core (inner and outer), mantle, crust, internal structure, chemical composition of Earth

Grade 12

Parent/daughter isotope, alpha particle, beta decay, gamma decay, gravity, magma

Empirical Laws or Observed Relationships:

Law of universal gravitation, inverse square law for radiation, exponential absorption law for radiation, Earth=s internal heat flux as a function of the age of ocean floors or continental regions

Theories or Models:

Mantle convection, evolution of Earth (physical), structure of Earth=s interior

Page 81 in

Micro-Unit Description:

Radioactivity, Time and Age
Students should develop an understanding of average lifetime for a radioactive material expressed in terms of half-life (1.433T1/2). They should use results of such calculations for various radioactive materials to consider implications for radioactive wastes. (b) Using radioactive count data in a graph, students should determine half-life and mean lifetime of a radioactive sample. (c) Students should create and examine macroscopic analogs to chain reactions, like mousetrap/Ping Pongtm ball arrangements, to gain the concept of a chain reaction. (d) Grade nine students should learn to use the concept of geologic time in relationship to fossils.

National Science Teachers Association
1840 Wilson Boulevard
Arlington VA 22201-3000