HALF-LIFE

The rate of decay for a radioactive isotope varies considerably. The half-life of a radioisotope is constant and independent of the sample size. The time that it takes for half of any sample to decay is called the half-life.

NOTE: has a half-life of 4.5 billion years. Very old rock samples can be dated based on their content.

The oldest rock found on earth (in Greenland) was dated 3.7 billion years. The solar system has an estimated age of 4.6 billion years based on dating meteorites.

EXAMPLE C

Barium-122 has a half-life of 2 minutes. A fresh sample weighing 80 g 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?

EXAMPLE D
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.

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.

EXAMPLE E

Carbon-14 has a half-life of 5730 years and is used to date archaeological objects.

All living organisms have a constant carbon-12/carbon-14 ratio. When the organism dies carbon-12 levels remain constant but carbon-14 decays. The changing carbon-12/carbon-14 ratio can be used to determine the date of the artifact. For example, fresh charcoal made from a tree contains carbon-14 which will give a radioactive count of 13.60 disintegrations per minute per gram of carbon. Prehistoric cave paintings were found in Spain. A piece of charcoal found in the ancient cave in Altamira, Spain gave 1.70 disintegrations per minute per gram of carbon. From this information, determine the age of the cave paintings. After one half-life the number of disintegrations will go from 13.60 to 6.80; after two half-lives it is 3.40 and after three half-lives 1.70. Therefore 3 half-lives have elapsed since the paintings were done. Since the half-life of carbon-14 is 5730 years the paintings are about 5730x3=17,190 years old.

PROBLEM 4:
Perform the following problems

a. 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?

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b. The half-life of carbon-14 is 5730 years. A piece of linen found today contains carbon-14 and gives an activity of 15 counts per minute per gram of carbon. If an anthropologist found an ancient piece of linen believed to date back to the Neolithic period which gave only 7.5 counts per minute per gram of carbon, how old is the ancient linen ?

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c. Technetium-99m is used for brain scans. If a laboratory receives a shipment of 200 g of this isotope and after 24 hours only 12.5 g of this isotope remain, what is the half-life of technetium-99m?

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d. Mercury -197 is used for kidney scans and has a half-life of 3 days. If the amount of mercury-197 needed for a study is 1.0 gram and the time allowed for shipment is 15 days, how much mercury-197 will need to be ordered?

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e. The half-life of strontium-90 is 25 years. How much strontium-90 will remain after 100 years if the initial amount is 4.0 g?

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f. If the half-life of uranium-232 is 70 years, how many half-lives will it take for 10 g of it to be reduced to 1.25 g?

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a. 12.5 g            Click here to return to problems

b. 5730 years           Click here to return to problems

c. 6 hours           Click here to return to problems

d. 32 g           Click here to return to problems

e. 0.25 g           Click here to return to problems

f. 3 half-lives           Click here to return to problems