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## Half-Life

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**Half-Life**Half-life is the time required for half of a sample of a radioactive substance to disintegrate by radioactive decay. Atoms with shorter half-lives are more unstable. The half-life of an isotope is not affected by heat, pressure or any other physical means.**Half-life is used by scientists to predict the age of an**object. • The isotope C-14 is used to date materials that were once living or came from living things. • C-14 has a half life of 5715 yrs. This means that after 5715 yrs, a 100 gram sample of C-14 will be half C-14 and half some other isotope. After 11430 yrs, the sample will be 25 g C-14 and 75 grams of some other isotope.**Half-life Problems**• In many problems, you will be given the total (elapsed) time and the length of one half-life. You have to determine the number of half-lives before working the problem. • To find the number of half-lives divide the elapsed time by the length of one half-live. • Ex. If one half-life is 8 days, and 24 days have gone by, how many half-lives have occurred?**Half-life Problems**• Number of half-lives will be represented by n • Original mass of substance will be mi • Final mass of substance will be mf • Formula: mf = --------- mi 2n**1. How much of a 100 g sample of Rn-222 is left after 15.2**days if its half life is 3.8 days? First find the number of half-lives that have occurred. Divide 15.2 days by 3.8 days to get the number of half lives: Givens: Hint: n =number of half lives, mi= original mass mf = final mass**1. How much of a 100 g sample of Rn-222 is left after 15.2**days if its half life is 3.8 days? First find the number of half-lives that have occurred. Divide 15.2 days by 3.8 days to get the number of half lives: 4 Givens: n = 4 mi = 100 g mf = ? mi Formula mf = -------- mf = -------- 2n**1. How much of a 100 g sample of Rn-222 is left after 15.2**days if its half life is 3.8 days? First find the number of half-lives that have occurred. Divide 15.2 days by 3.8 days to get the number of half lives: 4 Givens: n = 4 mi = 100 g mf = ? mi Formula mf = -------- mf = -------- = -------- = 2n 100 g 16 100 g 24**2. How much of a 200 g sample of I-131 is left after 16 days**if its half life is 8 days? First find the number of half-lives that have occurred Givens: n = mi = mf = ? Formula : mf = -------- n =number of half lives, mi = original mass mf = final mass**How much of a 200 g sample of I-131 is left after 16 days if**its half life is 8 days? First find the number of half-lives that have occurred Givens: n = 2 mi = 200 mf = ? Formula : mf = -------- mf = ----------- = n =number of half lives, mi = original mass mf = final mass mi 2n**2. How much of a 200 g sample of I-131 is left after 16 days**if its half life is 8 days? First find the number of half-lives that have occurred Givens: n = 2 mi = 200g mf = ? Formula : mf = -------- mf = ----------- = n =number of half lives, mi = original mass mf = final mass mi 2n 200g 22 200g 4**To Find Original Amount**• Rearrange the basic equation so that mi is by itself on one side of the equals sign. • mi = mf x 2n • 3. The half life of Iodine-131 is 8 days. If after 24 days there are 6.25 grams of Iodine-131 left. How much was in the original sample? n = mf = mi =**4. If the half life of a radioactive sample is 4.0 days and**8 grams is left after 20 days, how much did you start with?**6. How many half-lives will it take for 160 grams to be**reduced to 40 grams?**Sometimes you will be given the percent or fractional**amount that remains or has decayed instead of the number of days. • To find the number of half lives multiply by ½ until you get the percent or fractional amount that remains • EX: If the problems says that 1/32 remains, multiply ½ x ½ x ½ x ½ x ½ until you get 1/32. The number of half lives will be 5. • Ex: If the problem says that 7/8 has decayed, you must determine that 1/8 remains, then multiply ½ x ½ x ½ until you get 1/8. The number of half-lives will be 3.**Ra-226 has a half life of 1599 years. How long would it**take 15/16 of a Ra-226 sample to decay? First determine how much remains: 16/16-15/16 = 1/16 Then determine number of half-lives by multiplying ½ by itself until you get 1/16. ½ x ½ x ½ x ½ = 1/16 Count the number of ½s, so 4 half-lives have gone by. Multiply 4 x the half life of 1599 years: 4 x 1599 = 6396 years