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Half-Life
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Half-Life The half-life of a radioisotope is the time required for half the atoms in a given sample to undergo radioactive, or nuclear, decay. Half-life is given the symbol t½ Different radioisotopes have different half-lives. The amount of radioactive isotope remaining can be calculated: Nt = No x (0.5)number of half-lives Where: Nt = amount of radioisotope remaining No = original amount of radioisotope number of half-lives = time ÷ half-life
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Examples Consider strontium-90 which has a half-life of approximately 28 years. Initially, at time t=0, the sample is 100% strontium-90 After 28 years, only half the original amount of strontium will remain: ½ x 100% = 50% After another 28 years, only half of this amount of strontium-90 will remain: ½ x 50% = 25% After another 28 years, only half of this amount of strontium will remain: ½ x 25% = 12.5% and so on. At any given time, the amount of strontium-90 that has undergone decay can be calculated: amount of strontium-90 decayed = the original amount - the amount remaining.
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% Strontium-90 remaining
Number of Half-lives Time (years) % Strontium-90 remaining % Strontium-90 that has decayed 100 1 28 50 2 56 25 75 3 84 12.5 87.5 4 112 6.25 93.75 5 140 3.125 96.875 6 168 1.5625
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Calculate the percentage of strontium-90 remaining after 280 years.
1)What are we looking for? Remaining sample 2)What do we know? Nt = ? % No = 100% number of half-lives = 10 (time ÷ half-life = 280 ÷ 28 =10) 3) What is the formula? Formula: Nt = No x (0.5)number of half-lives 4) Solve. Nt = 100 x (0.5)10 = 0.098%
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Practice solving problems:
Ex: The radioisotope Tc-99m is used in bone scans. Tc-99 has a half-life of 6 hours. If a dose of 100 mg is given to the patient, how much sample remains in the body of a patient that had a Tc-99m bone scan after 24 hours?
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Bell Work: Ex: The half-life of radium-226 is 1,600 years. How many milligrams of radium-226 remain after 8,000 years if the original sample is mg? The half-life of iodine-131 is 8 days. How many milligrams of iodine-131 remain after 48 days if the original sample was 100 mg? Radon-222 has a half-life of 4 days. After 16 days, you have 6.25 mg of given sample of radon left. How much radon was in the original sample?
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