Nuclear Chemistry II. Radioactive Decay C. Half-Life II. Radioactive Decay C. Half-Life

C. Johannesson C. Half-life  Half-life (t ½ )  Time required for half the atoms of a radioactive nuclide to decay.  Shorter half-life = less stable.

C. Half-life Iodine-131 is used to treat thyroid cancer. The half-life of I-131 is 8 days. 24 days ago, a doctor obtained a 48 g sample of I-131. How many grams of I- 131 remain? 24 days / 8 days = 3 half-lives 1 st decay: 48g ÷ 2 = 24g 2 nd decay: 24g ÷ 2 = 12g 3 rd decay: 12g ÷ 2 = 6g

C. Half-life 1.time elapsed / t ½ = # half-lives elapsed (Let’s call # half-lives elapsed “n”) 2.Original amount / 2 n = final amount 24 days / 8 days = 3 half-lives 1 st decay: 48g ÷ 2 = 24g 2 nd decay: 24g ÷ 2 = 12g 3 rd decay: 12g ÷ 2 = 6g

C. Half-life A f :final amount of sample A i :initial amount of sample n:# of half-lives elapsed

C. Johannesson C. Half-life  Fluorine-21 has a half-life of 5.0 seconds. If you start with 25 g of fluorine-21, how many grams would remain after 60.0 s? GIVEN: t ½ = 5.0 s m i = 25 g m f = ? total time = 60.0 s n = 60.0s ÷ 5.0s =12 WORK : m f = m i (½) n m f = (25 g)(0.5) 12 m f = g

C. Half-life Carbon-14 is used to “carbon-date” some archaeological specimens. The half-life of carbon-14 is 5730 years. A certain fossil contains only 6.25% of the carbon-14 present in a living specimen. How many half-lives have passed? 1) 100÷2 = 50 2) 50÷2 = 25 3) 25÷2 = ) 12.5÷2 = 6.25

C. Half-life The half-life of carbon-14 is 5730 years. If 4 half-lives have passed, how many years old is this specimen? 4 x 5730 years = years n  t ½ = time elapsed (# half-lives elapsed = n)

C. Half-life n:# of half-lives elapsed t 1/2 :half-life of nuclide t total :time elapsed Time units must match!