Radiometric Dating: Understanding Decay and Time Measurement

This assignment introduces radiometric dating, a method for determining the absolute age of rocks and minerals, without delving into complex mathematical calculations. We'll focus on the fundamental logic behind the process and how the rate of radioactive decay is used to measure time. Here's a breakdown of the key concepts:

1. Parent-Daughter Relationship: For every parent isotope that decays, a daughter isotope is created.
2. Non-Linear Decay: The rate of radioactive decay is not constant over time. The number of decays in a given time period depends on the number of parent isotopes present. This concept leads to the idea of half-life (t 1/2), which is the time required for half of the parent isotope to decay into its stable daughter.

To visualize this process, we'll create a Parent-Daughter vs. Time graph. This graph illustrates two important points:

1. The intersection of the parent and daughter curves represents a half-life, where both have an equal number of atoms.
2. The graph visually demonstrates the change in the Parent-Daughter ratio over time. As each half-life passes, the number of parent atoms decreases while the number of daughter atoms increases.

Graphing the Decay

Plot the parent and daughter curves on the graph below based on the provided data. The Y-axis represents the concentration (in percentage), and the X-axis represents the number of half-lives.

| No. of Half-lives | Parent | Daughter | |---|---|---| | 1 | 50 | 50 | | 2 | 25 | 75 | | 3 | 12.5 | 87.5 | | 4 | 6.25 | 93.75 | | 5 | 3.125 | 96.875 | | 6 | 1.563 | 98.437 |

Determining Mineral Age

Use the graph you just created to answer the following questions.

Common Radiometric Isotopes

| Isotope Pair | Amount of Parent Isotope Remaining (%) | Amount of Stable Daughter Isotope Produced (%) | No. of Half-lives Measured | Half-Life (Years) | Age of Mineral | |---|---|---|---|---|---| | 238U & 206Pb | 50 | 50 | | 4.5 billion | | | 235U & Pb207 | 25 | 75 | | 713 million | | | 232Th & 208Pb | 90 | 10 | | 14.1 billion | | | 87Rb & 87Sr | 75 | 25 | | 47 billion | | | 40K & 40Ar | 40 | 60 | | 1.3 billion | | | 14C & 14N | 10 | 90 | | 5730 | |

How did you determine the age of the mineral that contains a particular radioactive isotope parent-daughter pair? ________________________________________________________________________

Radiometric Dating Exercise

This exercise will apply radiometric dating principles to determine the absolute ages of three different rocks (A, B, and C) in a geologic cross-section. The data in Table 1 represents isotopic analyses conducted on minerals from each rock unit.

TABLE 1. Results of Isotopic Analyses:

| Rock Unit | Number of Parent Atoms | Number of Daughter Atoms | |---|---|---| | A | 7497 | 1071 | | B | 11480 | 3827 | | C | 839 | 2517 |

We'll use the potassium-argon system, where potassium-40 has a half-life of 1.30 billion years. Show all your calculations and box your final answers.

1. What is the absolute age of the basaltic dike (unit A)?

2. What is the absolute age of the granite (unit B)?

3. What is the absolute age of the folded metamorphic rock (unit C)?

4. Compare your measured ages to the principles of relative dating. Would the order of the observed layers make sense? Explain your answer using the principles of relative dating.

Answers:

1. To find the absolute age of the basaltic dike, we use the following formula: Age = (t 1/2) x log(Po/Pt) where t 1/2 = 1.3 billion years, Po = 7497, Pt = 1071, and Dt = 6426 (since the total number of atoms today equals the original number of parent atoms). Plugging in the values, we get: Age = (1.3 billion years) x log(7497/1071) = 54.2 million years

Therefore, the absolute age of the basaltic dike is 54.2 million years.

2. For the granite, we use the same formula but with Po = 11480, Pt = 7653, and Dt = 3827. This gives us: Age = (1.3 billion years) x log(11480/7653) = 100.4 million years

Therefore, the absolute age of the granite is 100.4 million years.

3. For the folded metamorphic rock, we use the same formula with Po = 2517, Pt = 1678, and Dt = 839. This gives us: Age = (1.3 billion years) x log(2517/1678) = 223.5 million years

Therefore, the absolute age of the folded metamorphic rock is 223.5 million years.

4. The measured ages align with the principles of relative dating. The basaltic dike (A) is the youngest, followed by the granite (B), and then the folded metamorphic rock (C). This order is consistent with the principle of superposition, which states that in undisturbed rock layers, older rocks are found below younger rocks. Additionally, the relative ages are consistent with the principle of cross-cutting relationships, where a rock or feature cutting across another must be younger. In this case, the basaltic dike cuts across both the granite and the metamorphic rock, confirming its younger age.