15. Complete the table below to track how the proportion of parent and daughter isotopes, and the daughter/parent ratio, changes as a function of the number of half-lives that have elapsed. Remember that for each half-life one-half of the parent atoms decay to daughter atoms. We start at time zero with 100% parent and 0% daughter. After one half-life, half of the parents have decayed to daughters, so we have 50% parent and 50% daughter, a 1:1 ratio. After the next half life, one half of the parents remaining decay, so we now have 1/2 of 50% or 25% parent. The parents are decaying to the daughter isotope, so that means we now have 50% + 25% or 75% daughter. The ratio of parent to daughter would then be 3:1 (75/25). For each successive half life, we decay of the remaining parent isotopes and increase the proportion of daughter isotopes by the amount of parent that decayed 16. Samples containing organic matter can sometimes be dated using the decay of radioactive carbon- 14 to stable nitrogen-14. The number of parent (14C) and daughter (14N) isotopes have been measured in organic samples (charcoal from campfires) collected at three different archeological sites and are reported in the table below. Complete the table to date these samples using Carbon- 14 dating Determine the daughter/parent ratio by dividing the number of daughter atoms by the number of parent atoms (D/P). The D/P ratio is converted to half-lives elapsed using the graph below. Find the D/P ratio on the y-axis. Follow over to the curve, then down to the x-axis to find the corresponding half- lives elapsed to produce this ratio. Example: the D/P ratio is 12. The corresponding half-lives elapsed would be 3.7 Calculate the age of the sample in years by multiplying the half-life of 14C (5,730 years) by the half-lives that have elapsed. Using our example: at D/P ratio = 12, the half-lives elapsed would be 3.7, and so the age of the sample would be 5730 * 3.7 = 21,201 years 17. Would it be possible to use 14C age dating to estimate the age of a dinosaur bone? Explain. (1 pt) Hint: Dinosaurs became extinct 66.5 million years ago. Geologists must use radioisotopes with longer half-lives, such as the decay of 40K to 40Ar with a half- life of 1300 million years, to date older materials. 18. Glacial erosion has exposed very old Precambrian granite on the west coast of Greenland. A muscovite crystal from this granite was analyzed and found to contain 687 atoms of 40K and 2748 atoms of 40Ar. Using K-Ar dating, what is the age of this granite in years? (1 pt) Hint: follow the same steps you did above for radiocarbon dating. Once you have the half-lives elapsed, multiply by the half life of K-Ar, 1300 million years, rather than the half-life of C-14. Isotopic analysis of a granitic intrusion indicates that 25% of the original 40K is present. Analysis of a nearby basaltic intrusion indicates that 50% of the original amount of 40K is present. 19. What is the absolute age of the granitic intrusion.

1. 15. Complete the table below to track how the proportion of parent and daughter isotopes, and the
daughter/parent ratio, changes as a function of the number of half-lives that have elapsed.
Remember that for each half-life one-half of the parent atoms decay to daughter atoms. We
start at time zero with 100% parent and 0% daughter.
After one half-life, half of the parents have decayed to daughters, so we have 50% parent and
50% daughter, a 1:1 ratio.
After the next half life, one half of the parents remaining decay, so we now have 1/2 of 50%
or 25% parent. The parents are decaying to the daughter isotope, so that means we now have
50% + 25% or 75% daughter. The ratio of parent to daughter would then be 3:1 (75/25).
For each successive half life, we decay of the remaining parent isotopes and increase the
proportion of daughter isotopes by the amount of parent that decayed
16. Samples containing organic matter can sometimes be dated using the decay of radioactive
carbon-
14 to stable nitrogen-14. The number of parent (14C) and daughter (14N) isotopes have been
measured in organic samples (charcoal from campfires) collected at three different archeological
sites and are reported in the table below. Complete the table to date these samples using Carbon-
14 dating
Determine the daughter/parent ratio by dividing the number of daughter atoms by the number
of parent atoms (D/P).
The D/P ratio is converted to half-lives elapsed using the graph below. Find the D/P ratio on
the y-axis. Follow over to the curve, then down to the x-axis to find the corresponding half-
lives elapsed to produce this ratio. Example: the D/P ratio is 12. The corresponding half-lives
elapsed would be 3.7
Calculate the age of the sample in years by multiplying the half-life of 14C (5,730 years) by the
half-lives that have elapsed. Using our example: at D/P ratio = 12, the half-lives elapsed
would be 3.7, and so the age of the sample would be 5730 * 3.7 = 21,201 years
17. Would it be possible to use 14C age dating to estimate the age of a dinosaur bone? Explain. (1
pt)
Hint: Dinosaurs became extinct 66.5 million years ago.
Geologists must use radioisotopes with longer half-lives, such as the decay of 40K to 40Ar with a
half-
life of 1300 million years, to date older materials.
18. Glacial erosion has exposed very old Precambrian granite on the west coast of Greenland. A
muscovite crystal from this granite was analyzed and found to contain 687 atoms of 40K and 2748
atoms of 40Ar. Using K-Ar dating, what is the age of this granite in years? (1 pt)
Hint: follow the same steps you did above for radiocarbon dating. Once you have the half-lives
elapsed, multiply by the half life of K-Ar, 1300 million years, rather than the half-life of C-14.
Isotopic analysis of a granitic intrusion indicates that 25% of the original 40K is present. Analysis
of a
nearby basaltic intrusion indicates that 50% of the original amount of 40K is present.
19. What is the absolute age of the granitic intrusion (in years)? (1 pt)
Hint: proportion of parent atoms is 0.25, so the proportion of daughter atoms is 0.75. So the

2. D/P ratio would be 0.75 divided by 0.25. Then, find the half-lives elapsed and the age of the
sample using the half-life of K-Ar, 1300 million years.
20. What is the absolute age of the basaltic intrusion (in years)? (1 pt)
Hint: The proportion of parent atoms is 0.5, so then proportion of daughter atoms is also 0.5.
Find the D/P ratio, half-lives elapsed, and age as before.
21. The basaltic intrusion cuts through the granite. Does this make sense with the dates above?
Explain. (1 pt)
Hint: think about what the observed cross-cutting relationships tell you about the relative ages
of the basalt and granite.
The age of a rock or rock unit can be approached in two ways - relative time and absolute time.
Relative time only determines the age of rocks or geologic features with respect to each other. The
relative geologic time scale focuses on observations of the rock sequence and fossil record. Exact
chronological age of a rock is its absolute age. Absolute dating of rocks can be measured in years
using the decay of radioactive isotopes. As the radioactive parent isotopes in a mineral or rock
undergo the decay process, they are converted to more stable daughter isotopes. As the sample
ages, the number of parent atoms remaining decreases while the number of daughter atoms
produced increases. Therefore, the ratio of daughters to parents is a function of the age of the
sample, specifically the number of half-lives that have elapsed since its formation. The length of
the half-life (in years) for that particular parent-daughter decay pair can then be used to determine
the age of the sample. 15. Complete the table below to track how the proportion of parent and
daughter isotopes, and the daughter/parent ratio, changes as a function of the number of half-lives
that have elapsed. (1 pts) - Remember that for each half-life one-half of the parent atoms decay to
daughter atoms. We start at time zero with 100% parent and 0% daughter. - After one half-life, half
of the parents have decayed to daughters, so we have 50% parent and 50% daughter, a 1:1 ratio.
- After the next half life, one half of the parents remaining decay, so we now have 1/2 of 50% or
25% parent. The parents are decaying to the daughter isotope, so that means we now have 50%+
25% or 75% daughter. The ratio of parent to daughter would then be 3:1 (75/25). - For each
successive half-life, we decay 1/2 of the remaining parent isotopes and increase the proportion of
daughter isotopes by the amount of parent that decayed.16. Samples containing organic matter
can sometimes be dated using the decay of radioactive carbon14 to stable nitrogen-14. The
number of parent (4C) and daughter (N) isotopes have been measured in organic samples
(charcoal from campfires) collected at three different archeological sites and are reported in the
table below. Complete the table to date these samples using Carbon14 dating ( 3 pts): - Determine
the daughter/parent ratio by dividing the number of daughter atoms by the number of parent atoms
(D/P). - The D/P ratio is converted to half-lives elapsed using the graph below. Find the D/P ratio
on the y-axis. Follow over to the curve, then down to the x-axis to find the corresponding halflives
elapsed to produce this ratio. Example: the D/P ratio is 12 . The corresponding half-lives elapsed
would be 3.7 - Calculate the age of the sample in years by multiplying the half-life of 24C(5,730
years) by the half-lives that have elapsed. Using our example: at D/P ratio =12, the half-lives
elapsed would be 3.7 , and so the age of the sample would be 57303.7=21,201 years. The ability
to use a particular radioisotope for dating depends on the useful age range of that isotope. As the
isotope decays, parents are converted to daughters. The age is determined by measuring the ratio

3. of daughters to parents, and relating that measurement to the number of half-lives that have
passed for that particular sample to determine its age. So, to make the necessary measurements,
the sample needs to have a sufficient number of both parents and daughters for accurate
measurement. So, an isotope with a relatively short half-life cannot be used to date very old
materials because therewill not be enough of the parent isotope left to measure. Such a sample
would have an infinite age because as the number of parent atoms approaches zero, the ratio
daughter/parent approaches infinity. As a general rule, the sample must be younger than 1012
half-lives to be dated using that particular isotope, otherwise there will be too few parent atoms left
to measure. Likewise, isotopes with very long half-lives cannot be used to date young materials
because not enough daughter atoms have been produced for measurement. 17. Would it be
possible to use 24C age dating to estimate the age of a dinosaur bone? Explain. (1 pt) Hint:
Dinosaurs became extinct 66.5 million years ago. Geologists must use radioisotopes with longer
half-lives, such as the decay of K to 20 Ar with a halflife of 1300 million years, to date older
materials. 18. Glacial erosion has exposed very old Precambrian granite on the west coast of
Greenland. A muscovite crystal from this granite was analyzed and found to contain 687 atoms of
40K and 2748 atoms of 1) Ar. Using KAr dating, what is the age of this granite in years? (1 pt)
Hint: follow the same steps you did above for radiocarbon dating. Once you have the half-lives
elapsed, multiply by the half -life of K-Ar, 1300 million years, rather than the half-life of C14.
Isotopic analysis of a granitic intrusion indicates that 25% of the original K is present. Analysis of a
nearby basaltic intrusion indicates that 50% of the original amount of K is present. 19. What is the
absolute age of the granitic intrusion (in years)? (1 Pt) Hint: proportion of parent atoms is 0.25 , so
the proportion of daughter atoms is 0.75 . So the D/P ratio would be 0.75 divided by 0.25 . Then,
find the half-lives elapsed and the age of the sample using the half-life of KAr,1300 million years.
20. What is the absolute age of the basaltic intrusion (in years)? (1 pt) Hint: The proportion of
parent atoms is 0.5 , so then proportion of daughter atoms is also 0.5 . Find the D/P ratio, half-
lives elapsed, and age as before. 21. The basaltic intrusion cuts through the granite. Does this
make sense with the dates above? Explain. (1 pt) Hint: think about what the observed cross-
cutting relationships tell you about the relative ages of the basalt and granite.