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Clip

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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, y-ray

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

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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

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

Half

lives

% 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

Half

lives

% 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

Half

lives

% 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

Half

lives

% 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)

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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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Answers to Half-Life Calculations

•Half-Life Calculation #1– 6.25 mgSTEP 1 divide 30 by 5. You get 6. This means it is going to divide 6 times

STEP 2

• Divide 400 6 times• 400 / 2 = 200• 200 / 2 = 100• 100 / 2 = 50• 50 / 2 = 25• 25 / 2 = 12.5• 12.5 / 2 = 6.25 mg

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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.

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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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Answers to Half-Life Calculations

•Half-Life Calculation #2– 12.5 mg

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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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Answers to Half-Life Calculations

•Half-Life Calculation #3– 750 mg

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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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Answers to Half-Life Calculations

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

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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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Answers to Half-Life Calculations

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

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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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Answers to Half-Life Calculations

•Half-Life Calculation #6– 15 minutes

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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 #7– 10 seconds