Radioactivity Lab Prompt• You have been given a fossil that according

to modern organisms should contain 128 g of carbon-14.  The fossil only contains 0.5g.  The fossil also should have contained at death 2.15 E-11g of radium-226.  Upon testing the fossil is has less than 8 E-20 g.  Using research and mathematics, determine the age of the fossil based on these two isotopes as well as answer the question of what other isotope might have given a more accurate age.

• It can be difficult to determine the ages of objects by sight alone.– Radioactivity provides a method to determine age by measuring

relative amounts of remaining radioactive material to stable products formed.

See pages 302 - 304

7.2 Half-life

• Carbon dating measures the ratio of carbon-12 and carbon-14.– Stable carbon-12 and radioactive carbon-14 exist naturally in a

constant ratio.– When an organism dies, carbon-14 stops being created and slowly

decays.• Carbon dating only works for organisms

less than 50 000 years old.

See pages 302 - 304

Using carbon dating, these cave paintings of horses,from France, were drawn 30 000 years ago.

7.2 Half-life

• Half-life measures the rate of radioactive decay.– Half-life = time required for half of the radioactive

sample to decay.– The half-life for a radioactive element is a constant

rate of decay.– Strontium-90 has a half-life of 29 years. If you have

10 g of strontium-90 today, there will be 5.0 g remaining in 29 years.

See pages 305 - 306

The Rate of Radioactive Decay

• Decay curves show the rate of decay for radioactive elements.– The curve shows the

relationship between half-life and percentage of original substance remaining.

See pages 305 - 306The decay curve for strontium-90

The Rate of Radioactive Decay

• There are many radioisotopes that can be used for dating.– Parent isotope = the original, radioactive material– Daughter isotope = the stable product of the

radioactive decay

See page 307

Common Isotope Pairs

– The rate of decay remains constant, but some elements require one step to decay while others decay over many steps before reaching a stable daughter isotope.• Carbon-14 decays into nitrogen-14 in one step.• Uranium-235 decays into lead-207 in 15 steps.• Thorium-235 decays into lead-208 in 10 steps.

(c) McGraw Hill Ryerson 2007 See page 307

Common Isotope Pairs

• Radioisotopes with very long half-lives can help determine the age of very old things.– The potassium-40/argon-40

clock has a half-life of 1.3 billion years.

– Argon-40 produced by the decay of potassium-40 becomes trapped in rock.

– Ratio of potassium-40 : argon-40 shows age of rock.

See pages 307 - 308

The Potassium-40 Clock

9

Radioactivity• An unstable atomic nucleus

emits a form of radiation (alpha, beta, or gamma) to become stable.

• In other words, the nucleus decays into a different atom.

10

Radioactivity• Alpha Particle – Helium

nucleus• Beta Particle – electron• Gamma Ray – high-energy

photon

11

Half-Life• Amount of time it takes for one

half of a sample of radioactive atoms to decay

12

Medical Applications of Half-Life

Nuclide Half-Life Area of BodyI–131 8.1 days ThyroidFe–59 45.1 days Red Blood CellsSr–87 2.8 hours BonesTc–99 6.0 hours Heart

Na–24 14.8 hours Circulatory System

Radioactive DecayRadioactive elements are unstable. They decay, change, into differentelements 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 howmuch 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 theage 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 – blue N14 - red

As we begin notice that no timehas gone by and that 100% of thematerial is C14

Halflives

% C14 %N14 Ratio of C14 to N14

0 100% 0% no ratio

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 – blue N14 - red

Halflives

% C14 %N14 Ratio of C14 to N14

0 100% 0% no ratio

1 50% 50% 1:1

After 1 half-life (5700 years), 50% ofthe C14 has decayed into N14. The ratioof C14 to N14 is 1:1. There are equalamounts 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 – blue N14 - red

Halflives

% C14 %N14 Ratio of C14 to N14

0 100% 0% no ratio

1 50% 50% 1:1

2 25% 75% 1:3

Now 2 half-lives have gone by for a totalof 11,400 years. Half of the C14 that waspresent at the end of half-life #1 has nowdecayed to N14. Notice the C:N ratio. Itwill 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 – blue N14 - red

Halflives

% C14 %N14 Ratio of C14 to N14

0 100% 0% no ratio

1 50% 50% 1:1

2 25% 75% 1:3

3 12.5% 87.5% 1:7

After 3 half-lives (17,100 years) only12.5% of the original C14 remains. Foreach half-life period half of the materialpresent decays. And again, notice the ratio, 1:7Age = 3 half lives (5700 x 3 = 17,100 yrs)

C14 – blue N14 - red How can we find the age of asample without knowing howmuch 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 halflife 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 ideahow much U238 was in the rock originally but allwe need is the U:Pb ratio in the rock today. Thiscan be obtained by standard laboratory techniques.

As you can see the U:Pb ratio is 1:1. From whatwe saw earlier a 1:1 ratio means that 1 half lifehas passed.Rock Sample

Now all we have to do is see what the half-life for U238 is. We canfind that information on page 1 of the reference tables.

Try the next one on your own.............orto review the previous frames click here.

1 half-life = 4.5 x 109 years (4.5 billion), so the rock is 4.5 billionyears old.

Element X (Blue) decays into Element Y (red)The half life of element X is2000 years.How old is our sample?

If you said that the sample was 8,000 years old, you understandradioactive dating.

If you’re unsure and want anexplanation just click.

See if this helps:1 HL = 1:1 ratio2 HL = 1:3 3 HL = 1:74 HL = 1:15

Element X (blue) Element Y (red)How old is our sample? We know that the sample wasoriginally 100% element X. There arethree questions:First: What is the X:Y ratio now?Second: How many half-lives had togo by to reach this ratio?Third: How many years does this number of half-lives represent?

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.

1) There is 1 blue square and 15 red squares. Count them. This is a 1:15 ratio.

Regents question may involvegraphs like this one. The mostcommon questions are:"What is the half-life of this element?"

Just remember that at the endof one half-life, 50% of theelement will remain. Find 50%on the vertical axis, Follow theblue line over to the red curveand drop straight down to findthe answer:

The half-life of this element is 1 million years.

Another common question is:"What percent of the materialoriginally present will remainafter 2 million years?"

Find 2 million years on thebottom, horizontal axis. Thenfollow the green line up to the red curve. Go to the left andfind the answer.

After 2 million years 25% of the original materialwill remain.

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 asthe age of the earth itself. That means that half the uranium originally present when the earthformed has now decayed. The half life of Rb87 is even longer.

Lastly, when you see a radioactive decay questionask yourself:> What is the ratio?> How many half-lives went by to reach this ratio?> How many years do those half-lives represent?

End Notes:

25

Half-Life Calculation #1• You have 400 mg of a

radioisotope with a half-life of 5 minutes. How much will be left after 30 minutes?

• Answer: 6.25 mg

26

Half-Life Calculation #2• Suppose you have a 100 mg

sample of Au-191, which has a half-life of 3.4 hours. How much will remain after 10.2 hours?

• Answer: 12.5 mg

27

Half-Life Calculation # 3• Cobalt-60 is a radioactive isotope

used in cancer treatment. Co-60 has a half-life of 5 years. If a hospital starts with a 1000 mg supply, how many mg will need to be purchased after 10 years to replenish the original supply?

• Answer: 750 mg