Logic statements governing radiometric dating

Use the simple logic statements governing radiometric dating (Parent -> Daughter + radiation + heat) and the rate of radioactive decay and build an understanding of radiometric decay and how it is used to measure time without mathematical calculations. From these logic statements some important concepts are emphasized:

1. First, for each parent isotope that decays one daughter isotope is created.
2. Secondly, it is important to notice in the rate expression that the number of decays is not a constant function of time (say for example the way a second is always 1/60th of a minute). Rather, the number of decays over a given time period changes with the number of parents present (simple example: 1/2 the students leave every 5 minutes during this lecture). Thus, decay is not a linear function of time, rather it is ‘curved’. The concept of half-life (t 1/2) is an important concept to remember. Half-life is the time required for half of the substance to decay to a stable daughter.

Given these basic points students can follow the construction of a Parent and Daughter vs. Time graph. This graph illustrates two major points regarding radiometric dating:

1. First, the point of intersection between the parent and daughter curves (both have equal no. of atoms) illustrates the concept of a half-life.
2. Second, this exercise graphically represents the change in Parent-Daughter ratio with time. With every half-life, there will be less parent atoms and correspondingly more daughters.

Plot the parent daughter curves on the graph below based on the values of their abundances with time (in half-lives). The purpose of this graph is to observe the rate of decay of a random isotope using the half-lives.
Your graph should have 2 lines, where the Y-axis is the concentration and the X-axis is the number of half-lives.
Isotope Pair concentration (%)
No. of Half-lives
1 2 3 4 5 6
Parent 50 25 12.5 6.25 3.125 1.563
Daughter 50 75 87.5 93.75 96.875 98.437

Determination of the ages of minerals using radiometric age dating. Use the curve you just constructed above to answer the questions below.
Common Radiometric Isotopes Amount of Parent Isotope Remaining (in %) 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? ____________________________________________________________

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Using Radiometric Dating to Help Determine the Geologic History of an Area.
RADIOMETRIC DATING EXERCISE

This project will introduce you to radiometric dating. You will be asked to calculate the absolute ages of three different rocks shown on the geologic cross-section below. These units are A–the basaltic dike, B–the granite, and C–the folded metamorphic rock (ignore the two sandstone layers for this exercise).

Isotopic analyses have been carried out on minerals separated from the three crystalline rocks A, B, and C. These data are listed below the cross-section in Table 1. To calculate the ages of the units, you will need to understand the principles of radiometric.

In this problem, we will be using the potassium-argon system; potassium-40 has a half-life of 1.30 billion years. Please show all of your mathematical work, and put a box around each of your final answers.

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

Radioactive parent isotopes decay at a constant rate and slowly become stable daughter isotopes. The decay rate is stated in terms of half-lives: the time it takes for one-half (50%) of the parent isotope to decay into the daughter isotope is called the half-life.

As the rock ages, the amount of the parent isotope will decrease and the amount of the daughter isotope will increase geometrically (not linearly). Graphs of radioactive decay clearly show this geometrical or exponential decay. To determine the age of an unknown rock, you need to measure the number of parent and daughter atoms in a sample (this data is given to you in the table). The ratio of the daughter atoms to the parent atoms is proportional to the age. But if you know the half-life as well as the number of atoms of both isotopes, you can calculate the age in years—an absolute age. You need to use the following formula:

P% is the percent of initial parent atoms remaining in the system
Po is the number of parent atoms originally present when the rock formed
Pt is the number of parent atoms today (see table)
Dt is the number of daughter atoms today (see table).

Obviously, the total of the parent and daughter atoms today is equal to the number of parent atoms when the rock formed, since each daughter atom came from a parent atom. When you divide the number of parent atoms today by the number of parent atoms originally, you will get a ratio, such as 1/4 (= 25%) or 1/2 (= 50%). This ratio is the percent of parent atoms remaining in the system today, and is directly related to the number of half-lives that have transpired since the rock crystallized from magma.

Please answer the following questions. Please show all your work: write your equations, values, and calculations.

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 initial chart. If you were to use the principles of relative dating, would the order of the observed layers make sense? Explain using the principles in your answer.

Plot of Parent Amount versus Time (in half-lives).

Sample Solution