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Radioactivity and Half-Life

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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.

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Radioactivity•Alpha Particle – Helium nucleus

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

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Half-Life•Amount of time it takes for one half of a sample of radioactive atoms to decay

http://www.absorblearning.com/media/item.action?quick=185

• Daughter isotope

• Decay curve• Half-life• Parent

isotope• Radiocarbon

dating

• 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

• 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.

• 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

• 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

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Medical Applications of Half-Life

Nuclide Half-Life Area of Body

I–131 8.1 days Thyroid

Fe–59 45.1 days Red Blood Cells

Sr–87 2.8 hours Bones

Tc–99 6.0 hours Heart

Na–24 14.8 hoursCirculatory

System

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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?

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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?

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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?

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Half-Life Calculation # 4•A radioisotope has a half-life of 1 hour. If you began with a 100 g sample of the element at noon, how much remains at 3 PM? At 6 PM? At 10 PM?

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Half-Life Calculation # 5•How many half-lives have passed if 255 g of Co-60 remain from a sample of 8160 g?

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Half-Life Calculation # 6•Suppose you have a sample containing 400 nuclei of a radioisotope. If only 25 nuclei remain after one hour, what is the half-life of the isotope?

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Half-Life Calculation # 7•If a radioactive element has diminished by 7/8 of its original amount in 30 seconds, what is its half-life?

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Answers to Half-Life Calculations

•Half-Life Calculation #1– 6.25 mg

•Half-Life Calculation #2– 12.5 mg

•Half-Life Calculation #3– 750 mg

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Answers to Half-Life Calculations

•Half-Life Calculation #4– 12.5 g, 1.5625 g, 0.09765625 g

•Half-Life Calculation #5– 5 half-lives

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Answers to Half-Life Calculations

•Half-Life Calculation #6– 15 minutes

•Half-Life Calculation #7– 10 seconds