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Half-Life Notes

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Half-Life: the amount of time it takes half of a radioactive sample to decay. Total Time Half-Life # Fraction of Radioactive Atoms Remaining Fraction of Radioactive Atoms Decayed 0 1 2 3 4 5 6 ½ ½ ¼ ¾ 1/8 7/8 1/16 15/16 1/32 31/32 1/64 63/64 10

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Example 1) Assuming a half-life of 1599 years, how many years will be needed for the decay of 15/16 of a given amount of radium-226? Need 4 half-lives 4 * 1599 years = 6396 years Total Time Half-Life # Fraction of Radioactive Atoms Remaining Fraction of Radioactive Atoms Decayed 0 1 2 3 4 ½ ½ ¼ ¾ 1/8 7/8 1/16 15/16 10 0 yrs 1599 yrs 3198 yrs 4797 yrs 6396 yrs

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Example 2) The half-life of radon-222 is 3.824 days. How much time must past for ¼ of a given amount of radon to remain? Need 2 half-lives 2 * 3.824 days= 7.648 days Total Time Half-Life # Fraction of Radioactive Atoms Remaining Fraction of Radioactive Atoms Decayed 0 1 2 ½ ½ ¼ ¾ 10 0 days 3.824 days 7.648 days

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Example 3) The half-life of polonium-218 is 3.0min. If you start with 16mg of polonium-218, how much time must pass for only 1.0mg to remain? Starting Amount = 16 mg Remaining Amount = 1.0 mg Fraction Remainig = 1.0 / 16 mg = 1/16 Total Time Half-Life # Fraction of Radioactive Atoms Remaining Fraction of Radioactive Atoms Decayed 0 1 2 3 4 ½ ½ ¼ ¾ 1/8 7/8 1/16 15/16 10 0 min 3.0 min 6.0 min 9.0 min 12 min Need 4 half-lives 4* 3.0min = 12 min

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After 4797 years, how much of an original 0.250g sample of radium-226 remains? Its half-life is 1599 years.

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The half-life of radium-224 is 3.66 days. What was the original mass of radium-224 if 0.0800g remains after 7.32 days?

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