Unit 2: The Atom Half- Life

Half Life The time required for one half of the nuclei of a radioactive isotope sample to decay to atoms of a new element. Half-lives can range from a fraction of a second to billions of years.. Ex) Half-life of 90 Sr is 29 years. If you had 10.0g of 90 Sr today, in 29 years how much would remain? Answer: 5.00g

Half-life Continued. After each half-life, only half of the sample remains Radioactive isotopes will decay until negligible amounts are present.

Calculating Half-life Amount remaining = (initial amt) x ( 1 / 2 ) n n = Total Time passed Length of one half-life Where n = the number of half life cycles that have passed.

Problem 59 Fe is used in medicine to diagnose blood disorders. The half-life of 59 Fe is 44.5 days. How much of a 2.00g sample will remain after 178 days? n= 178/ 44.5 n=4 amt remaining = (2.00) x ( 1 / 2 ) 4 amt remaining= 0.125g

Example #2 Nitrogen-13 decays to Carbon-13 and the half- life is 10 minutes. If you start with 2.0 grams of N-13, how many grams of N-13 will be left after 30 minutes have passed? t ½ = 10 mins Start Amt = 2.0 g Total time passed = 30mins Using the formulas n = total time / half life = 30min / 10min = 3 half lives Amt left = (2.0g) (½) 3 = (2.0) (½) (½) (½) = 0.25 g left.

Second Method – use a table Time # half lives amount left g 10 mins1 1.0 g 20 mins 20.5 grams 30 mins grams

Example #3 A 50 gram sample of nitrogen-16 decays to 12.5 grams in 14.4 seconds. What is the half-life of nitrogen –16? # half lives past = total time or t 1/2 = total time t 1/2 #half lives past # half lives pastAmt left 050g 125g g t 1/2 = 14.4 seconds 2 t 1/2 = 7.2 seconds

Example 4 If 100 grams of Au-198 is left after 8.10 days and the half-life is 2.70 days, what was the original amount present? # half lives past = total time t 1/2 Amount remaining = (initial amt) x (1/2) n 100 g = (x) (1/2) 3 = 8.10/2.7 = 3 X = 800 grams = original amount