Radioactivity
The internal heating machine is found deep inside the interior of the Earth. This internal furnace was formed at the heart of the planet some 4.6 billion years ago and is still operating today. It is fueled by the same type of residual heat and radioactivity that were present when the Earth and the other planets were formed. Scientists use a technique known as radiometric dating to determine the ages of planets, and thus the age of this internal heating machine. Radiometric dating is a technique used to date the ages of planets by analyzing samples of radioactive rocks and minerals. Radiometric dating is very reliable because it depends upon properties of the radioactive decay. All radioactive atoms, after a prescribed period of time, decay to half of the amount that was present at the beginning. This period of time for each atom is called its half-life. As the parent atom decays, the stable daughter atom increases proportionally.For example, the radioactive parent, Uranium 238, and its stable daughter, lead 206, reach a 1:1 ratio in about 4.5 billion years. Radiometric dating is a method used to determine the absolute age of a rock or a geologic event such as earthquakes or volcanoes. (Poort and Carlson, 32)
Radiometric dating is based on nuclear decay of naturally occurring radioactive isotopes such as uranium, potassium, rubidium and thorium and is applicable to all methods of age determination involving radioactive decay (Poort and Carlson, 32). Radioactive decay is the spontaneous disintegration of the isotopes of certain atoms into new isotopes until a stable isotope is reached. Certain types of particles are always emitted when an isotopic atom disintegrates. Alpha particles, Beta particles, and Gamma rays are generated during radioactive decay. Heat is always a by-product of radioactive decay, which produces the high temperatures of magma located at the Earth's core and volcanic lava flows.
Poort and Carlson (32) state that radioactive decay proceeds in several ways. Alpha decays occur when the nucleus of an atom emits an alpha particle composed of two protons and two neutrons. This loss changes both the atomic mass number (sum of protons and neutrons) and the atomic number (number of protons). A new element is formed when the atomic number is changed. For example, in the uranium decay series, the parent isotope Uranium-238 decays to the daughter isotope Thorium-234. Beta decay occurs when a neutron is converted to a proton through the loss of a high energy electron. The mass remains the same but the atomic number changes as in the decay of Rubidium-87 to Strontium-87. Poort and Carlson list electron capture as a form of radioactive decay. In this type of decay, an electron is incorporated by a proton in the nucleus. A proton is lost and a neutron is gained. Potassium-40 decays to Argon-40 since the atomic number changes and the atomic mass number remains the same.
The rate of radioactive decay is constant and can be determined from laboratory tests and use of decay curves. The decay rate is expressed in terms of a length of time called the half-life. Poort and Carlson (32) define a half-life as the amount of time necessary for half of the original parent atoms to decay to daughter products or atoms. After one half-life, one half of the original material is daughter products and the half is the remaining parent isotope. After the second half-life, one fourth of the original parent isotope remains. At this time in the teaching of the curriculum unit, I will have the students design a decay curve showing the half-life progression for radioactive isotopes such as U-235, U-238, Potassium-40, and Carbon-14. (Lesson 1, Activity 1). Students will discuss which isotopes are more useful for dating certain ages of rocks, planets, and events that have occurred during the last 40,000 years. The purpose of this assignment is to have students realize that each radioactive isotope has its own half-life. To date the age of the Earth, U-238, with a half-life of approximately 4.5 billion years, would be used. Potassium has a long half-life of 1.3 billion years. U-235 has a half-life of nearly 713 million years. Carbon-14 has a half-life of 5730 years and is useful in dating events occurring recently in Earth's history.
The relationship between lapsed time and the radioactive decay of an isotope is expressed by the mathematical formula (N= Noe - & L a m b d a ; t).
- N = number of atoms
- No= original number of atoms of the isotope
- e = mathematical constant 2.718
- Λ= decay constant
- thl =the half-life,
- Λ=decay constant
- t = age of the rock.
At this point in the unit, I will include exercises that require students to calculate the ages of rocks mathematically and theoretically (Lesson 1 Activity 2). Students may be given tagged rock samples containing descriptive data useful for calculating the ages of the rock samples. For example, I will give the student a faux rock sample containing both a parent-isotope X and its daughter-isotope Y. The parent X has a half-life of 80 million years. The students have a copy of the rock analysis from the Universal Geochronology Laboratory showing the following results: one-fourth of the total is parent X and three-fourth of the sample is daughter Y. The students will find the age of the rock whose half-life is 80 million years. The number of half-lives which have elapsed is 2. This number (2) may be found by using a decay curve.
Calculation for the age of the rock may be found by multiplying 2 half-lives x 80 million years. The age of this rock sample is 160 million years. Students may now complete the lesson on Dating Rocks Using the Decay Process?
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