Laboratory 8 Procedure:  Radiation

The impact of the radiocarbon dating technique on modern man has made it one of the most significant discoveries of the 20th century. No other scientific method has managed to revolutionize man’s understanding not only of his present but also of events that already happened thousands of years ago. Archaeology and other human sciences use radiocarbon dating to prove or disprove theories. Over the years, carbon-14 dating has also found applications in geology, hydrology, geophysics, atmospheric science, oceanography, paleoclimatology and even biomedicine. Radiocarbon (carbon-14) is an isotope of the element carbon that is unstable and weakly radioactive. The stable isotopes are carbon-12 and carbon-13.

Carbon-14 is continually being formed in the upper atmosphere by the effect of cosmic ray neutrons on nitrogen-14 atoms. It is rapidly oxidized in air to form carbon dioxide and enters the global carbon cycle.

Plants and animals assimilate carbon-14 from carbon dioxide throughout their lifetimes. When they die, they stop exchanging carbon with the biosphere and their carbon-14 content then starts to decrease at a rate determined by the law of radioactive decay.

See the following reference for more information:

Team, ESRL Web. “ESRL Global Monitoring Division - Education and Outreach.” NOAA Earth System Research Laboratory, 1 Oct. 2005, www.esrl.noaa.gov/gmd/education/isotopes/decay.html.

 

The number of nuclei disintegrating per unit of time is called the rate of radioactive decay, and can be calculated from the following formula:

Rate = k N_t

Figure 1. Equation for the rate of radioactive decay, where Nt is the number of radioactive nuclei at the time t, and k is the decay rate constant for radioactive decay or decay constant.

 

 

Another important term is a half-life of a radioactive nucleus, that is defined as the time it takes for one –half of the nuclei in the sample to decay. The half-life is independent of the amount of the sample.

T_1/2  = 0.693 / k

Figure 2. Equation for the half-life of a radioactive nucleus, where k is a decay constant.

 

 

 

                                                          Figure 3. Example of Radioactive Decay curve.

 

 

There are couple of objectives of this lab:

 

1. To enhance your ability to understanding of the radioactive decay and a half-life
2. To familiarize you with the half-life curve.

 

 

Pre-Lab Questions:

 

Analyze Figure 3. Radioactive Decay curve presented and answer the following questions.

1. What property is listed on x-axis?
2. What property is listed on y-axis?
3. What is the total mass of the sample?
4. What is the mass of the half of the sample?
5. What time corresponds to the decay of the half of the sample?
6. What is the half-life of the sample?

 

 

 

Procedure:

 

Read pages 698 –704 of your textbook prior to completing the procedure.

 

Collecting Data – Part I

 

From the course home page, access the simulation environment by clicking on the Radioactive Dating Game.

https://phet.colorado.edu/sims/cheerpj/nuclear-physics/latest/nuclear-physics.html?simulation=radioactive-dating-game

 

1. After the simulation environment loads, click on the “Half-Life” Tab.
2. Select carbon-14 from the right menu.
3. Inspect the graph and record its estimated half-time below.

5500 half life in years

4. Select 10 carbon-14 atoms from the bucket and move them to the white workspace. The goal is to measure how many of them undergo the decay process up until they reach the carbon-14’s half-life. Record the number of atoms that decay prior to the half-life in the table below. (N_t)
5. Repeat your measurements for 20, 30, and 40 atoms.
6. Repeat steps 1-5 for uranium-238.
7. Calculate the average N_t value for each radioactive element and enter the values in the ‘Average’ column in the first table below.
8. Using the equation in Figure 2, calculate the decay constant and enter the values in the table below.
9. Using equation in Figure 1, calculate rate of the radioactive decay and enter the values in the table below.
    

Nt	Estimated t1/2 (years)	10 atoms	20 atoms	30 atoms	40 atoms	Average
Carbon-14	5500	3	11	13	20	11.75
Uranium-238	4.5x109	6	13	17	19	13.75

 

	Decay Constant	Rate of Decay
Carbon-14	?	?
Uranium-238	?	?

Collecting Data – Part II

1. Select the “Dating Game” tab at the top of the simulation. For this part of the simulation, you will collect data in an effort to determine the age of various types of matter using carbon dating. The table below contain the samples that will be tested.
2. Click and drag the probe to the ‘Living Tree’ near the animal skull. Notice that a dialog box will pop up once the probe is properly located over the sample. Record the percentage of carbon remaining in the table below.
3. Predict the age of the sample and record this in the table below. Check your answer in the dialog box.
4. Repeat steps 2 and 3 for the remaining samples.
5. Finish the lab by preparing a report.

Sample	% Carbon Remaining	Age of Sample (years)
Living Tree	100	0
Animal Skull	98.2	151
Wooden Cup	88.2	100
Bone	83.9	1460
Fish bones	14.4	1650
Rock 5	0.0	1.25 billion