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Comprehension Check #5: a) If a rock has 25% Potassium-40, what is the proportion of Argon-40? b) How many half-lives have elapsed? What is the age of the rock?

Comprehension Check #5: a) If a rock has 25% Potassium-40, what is the proportion of Argon-40? b) How many half-lives have elapsed? What is the age of the rock?

Applications and Investigations in Earth Science (9th Edition)
Applications and Investigations in Earth Science (9th Edition)
9th Edition
ISBN:9780134746241
Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Chapter1: The Study Of Minerals
Section: Chapter Questions
Problem 1LR
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**Table 1. Pairs of radioactive isotopes and representative half-lives as well as sample materials dated.** | Parent Isotope (P) | Daughter Isotope (D) | Half-Lives (T ½) | Materials Dated | |--------------------|----------------------|-------------------|----------------------------------------| | Uranium-238 | Lead-206 | 4.5 billion years | zircon | | Uranium-235 | Lead-207 | 713 million years | zircon | | Potassium-40 | Argon-40 | 1.3 billion years | biotite, muscovite, whole volcanic rock | | Carbon-14 | Nitrogen-14 | 5730 years | shells, wood, bones, limestone | **How was this discovered?** How do we know if an object is radioactive? The presence of radioactive atoms can be determined using a Geiger Counter as the energy and subatomic particles released during the decay of a radioactive parent to a daughter is detected. The early work of studying radioactivity showed that the amount of radioactive atoms seen or heard by the clicks on a Geiger Counter was proportional to the amount of radioactive atoms in the rock being measured. Now that we know the constant decay rates for different isotope pairs from Table 1 (as noted by T½ for the half-lives of these radioactive elements), we can determine the half-lives that have elapsed from parent to daughter ratios… and next calculate ages of rocks! **HOW TO DETERMINE THE AGE OF ROCKS** The number of parent atoms decreases as daughter atoms increase for each half-life that has elapsed. Thus, older rocks have more daughter products as more decay has occurred. The first step then is to determine the % parent compared to the % daughter as done before. Geologists can measure the amount of daughter atoms in a rock, and subtract from 100% to determine the proportion of parent atoms remaining, and then assess how many half-lives have elapsed using Table 2. Then the age equation can be used to calculate the age of a rock for a specific pair of isotopes given the decay constant and half-lives that have elapsed. For example, a rock that has 50% Carbon-14 and 50% Nitrogen-14 is 5730 years old (as it is 1 x T ½ for that isotope pair). If a rock instead
Transcribed Image Text:**Table 1. Pairs of radioactive isotopes and representative half-lives as well as sample materials dated.** | Parent Isotope (P) | Daughter Isotope (D) | Half-Lives (T ½) | Materials Dated | |--------------------|----------------------|-------------------|----------------------------------------| | Uranium-238 | Lead-206 | 4.5 billion years | zircon | | Uranium-235 | Lead-207 | 713 million years | zircon | | Potassium-40 | Argon-40 | 1.3 billion years | biotite, muscovite, whole volcanic rock | | Carbon-14 | Nitrogen-14 | 5730 years | shells, wood, bones, limestone | **How was this discovered?** How do we know if an object is radioactive? The presence of radioactive atoms can be determined using a Geiger Counter as the energy and subatomic particles released during the decay of a radioactive parent to a daughter is detected. The early work of studying radioactivity showed that the amount of radioactive atoms seen or heard by the clicks on a Geiger Counter was proportional to the amount of radioactive atoms in the rock being measured. Now that we know the constant decay rates for different isotope pairs from Table 1 (as noted by T½ for the half-lives of these radioactive elements), we can determine the half-lives that have elapsed from parent to daughter ratios… and next calculate ages of rocks! **HOW TO DETERMINE THE AGE OF ROCKS** The number of parent atoms decreases as daughter atoms increase for each half-life that has elapsed. Thus, older rocks have more daughter products as more decay has occurred. The first step then is to determine the % parent compared to the % daughter as done before. Geologists can measure the amount of daughter atoms in a rock, and subtract from 100% to determine the proportion of parent atoms remaining, and then assess how many half-lives have elapsed using Table 2. Then the age equation can be used to calculate the age of a rock for a specific pair of isotopes given the decay constant and half-lives that have elapsed. For example, a rock that has 50% Carbon-14 and 50% Nitrogen-14 is 5730 years old (as it is 1 x T ½ for that isotope pair). If a rock instead
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