Radioactive Decay Radioactive elements are unstable. They decay, change, into different elements over time. Here are some facts to remember: The half-life of an element is the time it takes for half of the material you started with to decay. Remember, it doesn’t matter how much you start with. After 1 half-life, half of it will have decayed. Each element has it’s own half-life ( page 1 of your reference table) Each element decays into a new element (see page 1) C14 decays into N14 while U238 decays into Pb206 (lead), etc. The half-life of each element is constant. It’s like a clock keeping perfect time. Now let’s see how we can use half-life to determine the age of a rock or other artifact.
The grid below represents a quantity of C14. Each time you click, one half-life goes by. Try it! C14 – blueN14 - red As we begin notice that no time has gone by and that 100% of the material is C14 Age = 0 half lives (5700 x 0 = 0 yrs)
The grid below represents a quantity of C14. Each time you click, one half-life goes by. Try it! C14 – blueN14 - red After 1 half-life (5700 years), 50% of the C14 has decayed into N14. The ratio of C14 to N14 is 1:1. There are equal amounts of the 2 elements. Age = 1 half lives (5700 x 1 = 5700 yrs)
The grid below represents a quantity of C14. Each time you click, one half-life goes by. Try it! C14 – blueN14 - red Now 2 half-lives have gone by for a total of 11,400 years. Half of the C14 that was present at the end of half-life #1 has now decayed to N14. Notice the C:N ratio. It will be useful later. Age = 2 half lives (5700 x 2 = 11,400 yrs)
The grid below represents a quantity of C14. Each time you click, one half-life goes by. Try it! C14 – blueN14 - red After 3 half-lives (17,100 years) only 12.5% of the original C14 remains. For each half-life period half of the material present decays. And again, notice the ratio, 1:7 Age = 3 half lives (5700 x 3 = 17,100 yrs)
C14 – blueN14 - red How can we find the age of a sample without knowing how much C14 was in it to begin with? 1) Send the sample to a lab which will determine the C14 : N14 ratio. 2) Use the ratio to determine how many half lives have gone by since the sample formed. Remember, 1:1 ratio = 1 half life 1:3 ratio = 2 half lives 1:7 ratio = 3 half lives In the example above, the ratio is 1:3. 3) Look up the half life on page 1 of your reference tables and multiply that that value times the number of half lives determined by the ratio. If the sample has a ratio of 1:3 that means it is 2 half lives old. If the half life of C14 is 5,700 years then the sample is 2 x 5,700 or 11,400 years old.
C14 has a short half life and can only be used on organic material. To date an ancient rock we use the uranium – lead method (U238 : Pb206). Here is our sample. Remember we have no idea how much U238 was in the rock originally but all we need is the U:Pb ratio in the rock today. This can be obtained by standard laboratory techniques. As you can see the U:Pb ratio is 1:1. From what we saw earlier a 1:1 ratio means that 1 half life has passed. Rock Sample Now all we have to do is see what the half-life for U238 is. We can find that information on page 1 of the reference tables. 1 half-life = 4.5 x 109 years (4.5 billion), so the rock is 4.5 billion years old. Try the next one on your own.............or to review the previous frames click here.
Element X (Blue) decays into Element Y (red) The half life of element X is 2000 years. How old is our sample? See if this helps: 1 HL = 1:1 ratio 2 HL = 1:3 3 HL = 1:7 4 HL = 1:15 If you said that the sample was 8,000 years old, you understand radioactive dating. If you’re unsure and want an explanation just click.
Element X (blue) Element Y (red) How old is our sample? We know that the sample was originally 100% element X. There are three questions: First: What is the X:Yratio now? Second: How many half-lives had to go by to reach this ratio? Third: How many years does this number of half-lives represent? 1) There is 1 blue square and 15 red squares. Count them. This is a 1:15 ratio. 2) As seen in the list on the previous slide, 4 half-lives must go by in order to reach a 1:15 ratio. 3) Since the half life of element X is 2,000 years, four half-lives would be 4 x 2,000 or 8,000 years. This is the age of the sample.
Regents question may involve graphs like this one. The most common questions are: "What is the half-life of this element?" Just remember that at the end of one half-life, 50% of the element will remain. Find 50% on the vertical axis, Follow the blue line over to the red curve and drop straight down to find the answer: The half-life of this element is 1 million years.
Another common question is: "What percent of the material originally present will remain after 2 million years?" Find 2 million years on the bottom, horizontal axis. Then follow the green line up to the red curve. Go to the left and find the answer. After 2 million years 25% of the original material will remain.
End Notes: Carbon 14 can only be used to date things that were once alive. This includes wood, articles of clothing made from animal skins, wool or cotton cloth, charcoal from an ancient hearth. But because the half-life of carbon 14 is relatively short the technique would be useless if the sample was extremely (millions of years) old. There would be too little C14 remaining to measure accurately. The other isotopes mentioned in the reference tables, K40, U238, and Rb87 are all used to date rocks. These elements have very long half-lives. The half-life of U238 for example is the same as the age of the earth itself. That means that half the uranium originally present when the earth formed has now decayed. The half life of Rb87 is even longer. Lastly, when you see a radioactive decay question ask yourself: > What is the ratio? > How many half-lives went by to reach this ratio? > How many years do those half-lives represent?