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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:

Coin Flipper — Text Version

A coin flipper interactive is shown. Inputting a number from 1 to 200 will generate a random number of coins that are heads up and tails up. Below are three sample sets:

Set One:

Heads 200 96 54 28 13 7 4 2 1 0

Tails 0 104 42 26 15 6 3 2 1

Set Two:

Heads 200 94 44 18 11 6 5 2 2 1

Tails 0 106 50 26 7 5 1 3 0 1

Set Three:

Heads 200 103 57 36 18 8 4 2 1 0

Tails 0 97 46 21 18 10 4 2 1

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.

Data Table

Half-life Number Number of Nuclei in the Sample Number of Nuclei in the Sample

That Have Decayed

Start  0

1

2

3

4

5

6

7

8

9

10

11

12

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 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.

3Repeat step 2 until all of the pennies have decayed.

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?

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?

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?

B .Approximately how much mass remains after 21.0 hours?

C. What is the half-life for this isotope?