Half-Life Of A Red Vine Investigation Introduction: Radioactive isotopes all decay at a constant rate. While some can decay rapidly, others may decay over thousands of years. We measure the rate of decay using a unit called the half-life. The half-life of an isotope is the time it takes for one half of the substance to decay. For example: Hydrogen-3 has a half-life of 12.3 years Polonium-210 has a half-life of 140 days Carbon-14 has a half-life of 5,730 years Radon-222 has a half-life of 3.82 days When we talk about decay, it does not mean that the isotope disappears; it actually changes into a new isotope. A radioactive isotope continues to decay until it reaches a stable isotope, a process that is called a decay series. The stable and most common form of carbon is Carbon-12. Its atomic number is 6, which means that the stable version has 6 protons and 6 neutrons, and a mass number of 12. Carbon-14 is a radioactive element which is formed in the earth’s atmosphere. Carbon-14 and Carbon-12 will have the same ratio within a living thing; but at death the Carbon-14-to-Carbon-12 ratio will start to change. What does this have to do with carbon dating? Carbon dating uses the relative amounts of Carbon-12 and Carbon-14 to determine the age of a sample. Since it takes almost 6000 years for Carbon-14 to decay into Nitrogen-14, we can use the amount still within the rock to give us an idea of how old the rock is! Guiding Questions: 1. Why do unstable atoms undergo radioactive decay? 2. How do we represent exponential radioactive decay graphically? Objective: In this activity, you will simulate the radioactive decay of an isotope using Red Vines and graph your results. Materials: Red Vine Ruler Knife Paper Towel Stopwatch Pre-Lab: 1. Where do nuclear reactions take place within an atom? 2. Why do isotopes undergo radioactive decay? (Hint: How does the mass & size of the nucleus change over time?) 3. Hypothesis: How would you represent the radioactive decay of an isotope on a graph? Teacher’s Initials:______ Procedures: 1. Assume that the half-life of a Red Vine is 30 seconds. This means that once you begin the lab, half of the Red Vine must decay every 30 seconds! Half-Life Of A Red Vine Investigation 2. Using a ruler, measure the length of your Red Vine in centimeters (cm) and record in the data table. This represents the length of time at 0 seconds (the beginning of the lab). 3. Label the x- and y-axis on your graph below and mark this beginning point on your graph. 4. Watch the clock or stopwatch. During the next 30 seconds, you must eat EXACTLY half of your Red Vine. Make sure to measure carefully with the ruler where half the Red Vine lies and cut using the knife. 5. Mark the length of the Red Vine now on the graph at the 30 second mark. 6. Repeat every 30 seconds, by halving your Red Vine. Stop when you get to 210 seconds! 7. Draw a smooth curve on your graph that connects all your points together. Data Table Length of Red Vine (cm) 0 sec 30 sec 60 sec 90 sec 120 sec 150 sec 180 sec 210 sec Analysis Questions: 1. How many half-lives did your Red Vine undergo as it decayed? Half-Life Of A Red Vine Investigation 2. At this rate, will the Red Vine ever disappear? Explain your answer using evidence from your graph. 3. If you had a giant, 1000 cm Red Vine, how much of it would remain after: a. One half-life:___________________ d. Four half-lives:_________________ b. Two half-lives:__________________ e. Five half-lives:_________________ c. Three half-lives:________________ f. Six half-lives:__________________ Use the following table to complete the remaining questions. Make sure to show your work! 4. Use the data in the table above to complete the following chart: 5. If you had 60 grams of Iodine-131, how much would remain after 24.21 days? Half-Lives 0 Time Elapsed 0 days Mass 60g 24.21 days 6. If 0.0625 g of Sodium-24 has decayed from a sample that was originally 2 g, how old is the sample? Half-Lives Time Elapsed Mass 7. Fluorine-21 has a half-life of approximately 5 seconds. What fraction of the original nucleus would remain after 1 minute? HalfLives Time Half-Life Of A Red Vine Investigation Fracti on 8. What fraction of Uranium-238 that was present when Earth was formed still remains if the Earth’s age is 4.5 x 109 years old? 9. A medical institution requests 1 g of Bismuth-212. About how many grams of Bismuth-212 must be prepared if the shipping time is 3 hours? Half-Lives Time Elapsed Mass 10. If we start with 60 atoms of Uranium-238, how many would remain after 9.0 x 109 years? Half-Lives Time Elapsed Atoms 11. A paleontologist unearths the remains of a Tyrannosaurus rex. We know that these dinosaurs became extinct about 65 million years ago. Therefore, would it be reasonable to expect that the Carbon-14 in the fossil has completed 15,000 half-lives? Why or why not? 12. An archaeologist finds a piece of old bone that she believes may be 2,000 years old. The lab technician tells her that the Carbon-14 in the bone has completed 25% of its first half-life. Does this finding support her belief about the age of the bone? Why or why not?
