Potassium-40 can decay into either calcium-40 or argon-40. All three of these at

Question

Potassium-40 can decay into either calcium-40 or argon-40. All three of these atoms have essentially the same weight. Ninety percent of the potassium-40 will decay into calcium-40, and only ten percent will decay into argon-40. When argon-40 is produced by the radioactive decay of potassium-40 inside a rock, the argon-40 produced by the decay is a gas and is trapped inside the rock. The amount argon-40 trapped in a rock can be measured by grinding up the rock and capturing the liberated argon-40 gas.

Suppose the amount of potassium-40 inside a rock is measured to be 0.81 milligrams, and the amount of argon-40 gas trapped in the rock is measured to be 0.377 milligrams.

1.              How much of the potassium-40 that was originally present inside the rock has undergone radioactive decay to produce argon-40?

2.              What is the total amount of potassium-40 that has undergone radioactive decay to produce both calcium-40 and argon-40?

3.              How much potassium-40 was originally present in the rock?

4.              What percentage of the potassium-40 originally present in the rock has not yet undergone radioactive decay?

5.              Use the decay curve for radioactive decay to determine how many half-lives of potassium-40 have elapsed since the rock formed?

6.              If the half-live of potassium-40 is 1.3 billion years, how long has it been since the rock formed?

Explanation / Answer

1. Since potassium 40 decays only 10% into Argon 40. Therefore the amount of potassium 40 that has undergone radioactive decay = 0.377 + 90% of 0.377 = 0.7163 milligrams

2. Total amount of Potassium 40 that has undergone radioactive decay is = 0.7163 milligrams

3. amount of potassium originally present is = 0.81 + 90% of 0.377 = 1.1493 milligrams

4. % of potassium 40 not undergone decay = 1.1493 - 0.81 / 1.1493 * 100 = 29.522 %

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