Half-Life Practice Problems
Question 1 The half-life of 222Rn is 4 days. After how many days is the amount remaining ¼ of the original amount?
Answer After 4 days ½ remains, after 8 days ½ of ½ (1/4) remains Answer: 8 Days
Question 2 The half-life of a material is 100 years. If you have 1,000 g, how much will remain after 500 years?
Answer After 100 years ½ remains After 200 years ¼ remains (1/2 of ½) 1/32 of 1000.0 g = 31.25g or (1000/32=31.25g)
Question 3 Barium-122 has a half-life of 2 minutes. A fresh sample weighing 80g was obtained. If it takes 10 minutes to set up an experiment using barium-122, how much barium-122 will be left when the experiment begins?
Answer Every half-life, 2 minutes, half of the original amount will undergo nuclear decay. Time Mass Start 80g 2 min 40g 4 min 20g 6 min 10g 8 min 5g 10 min 2.5g
Question 4 If 10 mg of iodine-131 is given to a patient, how much is left after 24 days? The half-life of iodine-131 is 8 days.
Answer Since the half-life is 8 days, 24 days corresponds to 3 half-lives. After one half- life 5 mg are left; after two half-lives, 2.5 mg; and after 3 half-lives 1.25 mg remain.
Question 5 Iodine-131 is used to destroy thyroid tissue in the treatment of an overactive thyroid. The half-life of iodine-131 is 8 days. If a hospital receives a shipment of 200 g of iodine-131, how much I-131 would remain after 32 days?
Answer 32 days/8days => 4 half-lives ½ x ½ = ¼ X ½ = 1/8 X ½ =1/16 200g/16 = 12.5g remain after 32 days
Question 6 An isotope of cesium (cesium-137) has a half-life of 30 years. If 1.0 mg of cesium-137 disintegrates over a period of 90 years, how many mg of cesium-137 would remain?
Answer 90 years/30 years = 3 half-lives ½ X ½ = ¼ X ½ = 1/8 remains of cesium-137 1.0 mg/8 = 0.125g remains of cesium-137
Question 7 Technetium-99 is used for brain scans. If a laboratory receives a shipment of 200g of this isotope and after 24 hours only 12.5g of this isotope remain, what is the half-life of technetium-99?
Answer 200/2 =100 100/2=50 50/2=25 25/2=12.5g => 4 half-lives 24hr/4= 6 hours