Absolute Dating

Table 1

Table 2

Table 3 and Graph 10, 8, 4, 0

Lab Question Answers Questions: 1, 2 (on table 5: a, b, c, d), 3, 4, 5, 6, 7, 8 8, 6.4, 3.2, 0

Conclusions 4, 3, 2, 0

Sources / Citations 2, 1.6, 1.2, 0

Activities for Lab 2: Absolute Dating

Activity 1: Isotope Pairs and Half Lives

NOTE: No additional materials are needed for this activity.

Instructions

Geologists use a variety of isotope pairs to date rocks and other materials using radioactive decay. In this activity, you will use the half-life values of the main isotope pairs to calculate the length of time represented by each half-life.

Table 1: Radioactive Isotope Pairs and Half-lives lists the various isotope pairs used on the left, and the length of one half-life for each pair. You are to determine the amount of time represented half-life values of 2, 3, 4, and 5. To do this, multiply the length of time for one half-life by the number of half-lives represented in each column. You will use this information to answer questions in other parts of this lab.

Table : Radioactive Isotope Pairs and Half-lives

Parent > Daughter Isotope Time needed for 1 half-life (years) Time needed for 2 half-life (years) Time needed for 3 half-life (years) Time needed for 4 half-life (years) Time needed for 5 half-life (years)

40K >40A 1.25 billion

238U > 206Pb 4.468 billion

235U > 207Pb 703.8 million

87Rb > 87Sr 48.8 million

14C > 14N 5,730

Activity 2: Using Probability to Predict Decay Rate

NOTE: No additional materials are needed for this activity.

Instructions

Scientists use mathematical concepts such as probability, to help them determine the theoretical outcomes for their models. In this activity, you are going to use the probability of the results of a coin toss to make predictions for the decay rate of a substance.

You will not actually be tossing a coin until Activity 3; in this activity you will use the probability of getting a heads to complete the data table. Since there are only two sides to a coin, the probability of getting a heads is one out of two – or one half. This means that if you flip a coin 10 times, the probability of getting a heads is 5 out of 10. The probability of the total number of heads varies with the amount of times you flip a coin, the probability of heads will be one half of the total flips. In the first row we will start at 100 because the “sample” is brand new. In the second row, we divide the value of Parent Material in the row above by 2 in order to get the half-life; this will also be the value for the Daughter Products; and for the final column you will simply sum the Daughter Products that have occurred.

You will be recording your probability predictions on Table 2: Predicting Decay Rates. The first part of the table has been completed for you; use these values to fill in the remaining cells.

On this table:

Time represents the number of half-lives that have passed since the beginning

Parent Material is the number of coins/flips you start with for each Half-life Time interval

Daughter Products is the number of Tails you flipped for each Half-life Time Interval

Cumulative Daughter Products column is a running total of how many daughter flips you have had (the values in this column should increase from 0 to 100).

Table : Predicting Decay Rates

Time

Representing Number of Half-lives Parent Material:

Predicted Number of Parents remaining for each time interval Daughter Products:

Predicted number of Daughters produced for each time interval Cumulative Total of Daughter

Products

0 100 0 0

1 50 50 50

2 25 25 75

3

4

5

6

7

Activity 3: Collecting Probability Data

Materials needed: Coin

Instructions

In activity 2, you predicted the probability of material remaining for seven half-lives. In this activity, you will be actually flipping the coin to collect real data that more closely reflects natural processes – nature rarely follows the rules exactly, usually because there are more variables involved than we humans are aware of. You will Record your results on Table 3: Decay Rates Based on Flipping a Coin. Notice that results obtained from two other fictional students who did this activity are included. You will be graphing all three sets of data.

Remember, for each flip: Heads = Parent Material, Tails = Daughter Products

For each Half-life Time Interval, start with the number of Parents left from the previous time interval. Repeat this procedure until there is no Parent Material Remaining, recording your results on Table 3: Decay Rates Based on Flipping a Coin.

Table : Decay Rates Based on Flipping a Coin

Your Data “Jason’s” Data “Brisell’s” Data

Time Parent Material Daughter Products

Cumulative Daughter

Products Time Parent Material Daughter Products

Cumulative Daughter

Products Time Parent Material Daughter Products

Cumulative Daughter

Products

0 100 0 0 0 100 0 0 0 100 0 0

1 1 48 52 52 1 49 51 51

2 2 28 20 72 2 26 23 74

3 3 5 23 95 3 15 11 85

4 4 4 1 96 4 6 9 94

5 5 2 2 98 5 5 1 95

6 6 1 1 99 6 2 3 98

7 7 0 1 100 7 1 1 99

Now that you have your data and the data of two additional students (Jason and Brisell), you are to graph your results.

Set up your graph in the following manner:

X-axis is the Manipulated/Independent Variable: Time values from 0 to 7, label your axis

Y-axis is the Responding/Dependent Variable: 0 to 100% of Parent Material, label your axis

Graph your results, using different colors or line types for the four sets of data. Include a key with your graph that indicates the symbol/color for each set of data:

Your Predictions from Activity 2

Your Data from Activity 3

“Jason’s” Data

“Brisell’s” Data

GRAPH:

Lab Questions for Lab 2: Absolute Dating

Activity 1: Isotope Pairs and Half Lives

1. Examine Table 4: Useful Geologic Material for Determining Age below. Using what you learned in Activity 1, explain how the Useful Dating Range was determined.

Table : Useful Geologic Materials for Determining Age

Parent > Daughter

Isotope

Applicable Geologic Materials Useful Dating range

40K >40A Potassium bearing minerals in igneous or

metamorphic rocks, e.g., Potassium-feldspar, Muscovite, Hornblende 100,000 to 4.5 billion years

238U > 206Pb