7.16 Radioactivity Dating Lab PDF

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Radioactivity Dating...

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Purpose: To explore half-life of a radioisotope Introduction: In this lab, you will investigate radiometric dating. The pennies represent the radio nuclide contained in our sample. An unstable nucleus decays in order to achieve a new nucleus that is either stable or a new nucleus that, in turn, will decay. This half-life is intrinsic to the isotope and cannot be altered by any extrinsic parameters such as temperature, pressure, or light. This decay of radioactive nuclei is a random event. The larger the number of radioactive nuclei, the closer the data will be to the probability of 50% of the sample decaying in one half-life. Each radio nuclide has its own characteristic half-life. Half-lives range from nanoseconds to billions of years. Materials: 200 pennies, Graphical Analysis. Alternative: Instead of pennies, you may use a bag of plain M&Ms® or the following interactive: Procedure: 1. Count the number of pennies and place this number in the data table under “Number of Nuclei in the Sample.” This number represents the total number of radioactive nuclei contained in our radioactive sample at the start. Place these pennies into a container. 2. Dump the pennies. The pennies that landed heads-up will represent decayed nuclei, the pennies tails-up are your remaining sample. Remove the “decayed” pennies. Count and the number of pennies that decayed and count the remaining pennies in the sample, and place the data in the appropriate column in the data table. 3. Repeat step 2 until all of the pennies have decayed. 4. Answer these questions.

Half-life Number

Number of Nuclei in the Sample

Start

Number of Nuclei in the Sample That Have Decayed 0

1

200

98

2

102

43

3

59

29

4

30

15

5

15

7

6

8

1

7

7

4

8

3

2

9

1

1

10

0

0

11

0

0

12

0

0

Questions: 1. Graph the “Number of Nuclei in the Sample” versus the “Half-life Number.” If the sample has 1/8 of the radioactive nuclei left, how many half-lives would the sample have gone through?

Gone through 3 half lives 2. Each time you dumped the pennies, one half-life passed; it has been shown that the half-life for this radioactive isotope is 20 years. In the year 2000, an archaeology team unearths pottery and is using this isotope for radiometric dating to place the age of the pottery. It is shown that 95% of the nuclei have decayed. Using your graph, approximately how long ago was the pottery made? At/Ao = 2^(-t/h) 0.05 = 2^(-t/20) t = 86.44 years 3. While investigating the half-life of a radioactive isotope, the following data was gathered. Graph the data; this graph should resemble the graph from your lab. Notice that you have a y-value at x = 0. This is called a decay curve. Answer the following questions: Time (hr)

Mass Remaining of the Isotope (g)

0.0

40.00

3.0

20.00

6.0

10.00

9.0

5.00

12.0

2.50

15.0

1.25

18.0

0.63

A. Approximately how much mass remains after 8.0 hours? i. After 8 hours approximately the mass remaining would be 6.667 B. Approximately how much mass remains after 21.0 hours? i. 0.63/2 = 0.315 C. What is the half-life for this isotope? i. 1/2...