The purpose of the remainder of this lab is to illustrate how absolute ages base
ID: 1325110 • Letter: T
Question
The purpose of the remainder of this lab is to illustrate how absolute ages based on radioactivity can be determined graphically. First, we will calculate and graph the daughter/parent ratio of isotopes in a theoretical rock. This first step is a theoretical model that can be applied to any radioactive element. Then we will use the graph we constructed, along with some real data, to determine the absolute ages for three real rock samples.
(a) First, complete the Parent Fraction and Daughter Fraction columns in Table 6-1. We'll start with 100% of parent material and 0% of daughter. After each half-life, half of the parent isotope has decayed (by definition), so start by dividing the parent fraction in half after each half-life elapsed. Since the parent isotope is turning into daughter isotope, the amount of parent that decays should then be added to the daughter fraction. Remember the sum of the two fractions must always equal 100%, so to figure out the daughter fraction, subtract the parent fraction from 100%. (For example, after one half-life, the parent fraction is 50% and the daughter fraction is 50%; after 2 half-lives, the parent fraction is 25% and the daughter fraction is 75%.)
(b) Next, complete the last column in Table 6-1 by dividing the Daughter Fraction by the corresponding Parent Fraction. For example, for 1 half-life elapsed:
This table holds true for any radioactive element, no matter how long its half-life is. (Consider again the definition of "half-life".)
1)
Table 6-1. Instructions for completing this table are above.
(Use these instructions to fill out Table 6-1 in the question below.)
2)
Table 6-2. Instructions for completing this table are above.
*Remember, one half-life for this particular radioactive element is 5,700 years.
Number of Half-Lives Elapsed Parent Fraction(%) Daughter Fraction
(%) Daughter/
Parent Ratio 0 100 0 0 1 50 50 1 2 25 75 3 4 5 The purpose of the remainder of this lab is to illustrate how absolute ages based on radioactivity can be determined graphically. First, we will calculate and graph the daughter/parent ratio of isotopes in a theoretical rock. This first step is a theoretical model that can be applied to any radioactive element. Then we will use the graph we constructed, along with some real data, to determine the absolute ages for three real rock samples. (a) First, complete the Parent Fraction and Daughter Fraction columns in Table 6-1. We'll start with 100% of parent material and 0% of daughter. After each half-life, half of the parent isotope has decayed (by definition), so start by dividing the parent fraction in half after each half - life elapsed. Since the parent isotope is turning into daughter isotope, the amount of parent that decays should then be added to the daughter fraction. Remember the sum of the two fractions must always equal 100%, so to figure out the daughter fraction, subtract the parent fraction from 100%. (For example, after one half - life, the parent fraction is 50% and the daughter fraction is 50%; after 2 half - lives, the parent fraction is 25% and the daughter fraction is 75%.) (b) Next, complete the last column in Table 6-1 by dividing the Daughter Fraction by the corresponding Parent Fraction. For example, for 1 half - life elapsed: This table holds true for any radioactive element, no matter how long its half - life is. (Consider again the definition of half - life.) 1) Table 6-1. Instructions for completing this table are above. Remember, one half - life for this particular radioactive element is 5,700 years.
Explanation / Answer
Table 6-1 Number of Half-lives elapsed Parent Fraction Daughter Fraction Daughter-Parent Ratio 0 100 0 0 1 50 50 1 2 25 75 3 3 12.5 87.5 7 4 6.25 93.75 15 5 3.125 96.875 31 Table 6-2 Sample Number of atoms of Parent Number of atoms of Daughter Daughter-Parent ratio Number fo half-lives elapsed Age in years A 2235 3303 1.4778 1.309 7461.6 B 4456 10725 2.406867 1.7684 10080 C 731 14690 20.095759 4.3988 25073
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