Which isotope pairs were originally used to determine the age of the Earth from meteorites? Be specific and be sure to write the numbers and the elements here as listed in Table 1.

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
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Which isotope pairs were originally used to determine the age of the Earth from meteorites?
Be specific and be sure to write the numbers and the elements here as listed in Table 1.
Transcribed Image Text:Which isotope pairs were originally used to determine the age of the Earth from meteorites? Be specific and be sure to write the numbers and the elements here as listed in Table 1.
Table 1. Pairs of radioactive isotopes and representative half-lives as well as sample materials dated.
Half-Lives (T1½)
Materials Dated
4.5 billion years
713 million years
1.3 billion years
5730 years
Parent Isotope (P) Daughter Isotope (D)
Uranium-238
Uranium-235
Potassium-40
Carbon-14
% Parent
100
91.7
Lead-206
Lead-207
Argon-40
Nitrogen-14
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 T 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!
84.1
70.7
50
35.4
25
HOW TO DETERMINE THE AGE OF ROCKS
The number of parent atoms decrease as daughter atoms increase for each half-life that has elapsed.
Thus, older rocks have more daughter product 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 had 75% Nitrogen-14, TWO half-lives have elapsed (parent
material is divided in half 2x leaving only 25% Carbon-14), and so the rock is 5730 x 2 = 11,460 years old.
Table 2. Decay parameters for all radioactive decay pairs and the age equations for half-lives elapsed.
Half-Lives Elapsed
12.5
6.2
% Daughter
0
8.3
15.9
29.3
zircon
zircon
50
64.6
75
87.5
93.8
biotite, muscovite, whole volcanic rock
shells, wood, bones, limestone
0
1/8
¼
½
1
1½
2
3
4
Age Equation
0xT½
0.125 x T ½
0.250 x T ½
0.500 x T ½
1.0 x T ½
1.5 x T ½
2.0 x T ½
3.0 x T ½
4.0 x T ½
Transcribed Image Text:Table 1. Pairs of radioactive isotopes and representative half-lives as well as sample materials dated. Half-Lives (T1½) Materials Dated 4.5 billion years 713 million years 1.3 billion years 5730 years Parent Isotope (P) Daughter Isotope (D) Uranium-238 Uranium-235 Potassium-40 Carbon-14 % Parent 100 91.7 Lead-206 Lead-207 Argon-40 Nitrogen-14 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 T 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! 84.1 70.7 50 35.4 25 HOW TO DETERMINE THE AGE OF ROCKS The number of parent atoms decrease as daughter atoms increase for each half-life that has elapsed. Thus, older rocks have more daughter product 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 had 75% Nitrogen-14, TWO half-lives have elapsed (parent material is divided in half 2x leaving only 25% Carbon-14), and so the rock is 5730 x 2 = 11,460 years old. Table 2. Decay parameters for all radioactive decay pairs and the age equations for half-lives elapsed. Half-Lives Elapsed 12.5 6.2 % Daughter 0 8.3 15.9 29.3 zircon zircon 50 64.6 75 87.5 93.8 biotite, muscovite, whole volcanic rock shells, wood, bones, limestone 0 1/8 ¼ ½ 1 1½ 2 3 4 Age Equation 0xT½ 0.125 x T ½ 0.250 x T ½ 0.500 x T ½ 1.0 x T ½ 1.5 x T ½ 2.0 x T ½ 3.0 x T ½ 4.0 x T ½
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