7.2 Half-Life7.2 Half-Life the time it takes for half of a radioactive the time it takes for half of a radioactive

sample to decaysample to decay– is a constant rate (always the same half life is a constant rate (always the same half life

for each element)for each element)

ExampleExample: Strontium-90 has a half-life of 29 : Strontium-90 has a half-life of 29 years. If you have 10 g of strontium-90 today, years. If you have 10 g of strontium-90 today, there will be 5 g (half) remaining in 29 years.there will be 5 g (half) remaining in 29 years.

Terminology:Terminology:Parent isotopeParent isotope: the original radioactive material: the original radioactive materialDaughter isotopeDaughter isotope: the stable product that : the stable product that

remains remains after decay has after decay has happenedhappened

Decay Curves:Decay Curves:

Show the rate of Show the rate of decay for radioactive decay for radioactive elementselements

show the relationship show the relationship between half-life and between half-life and percentage of original percentage of original substance remaining.substance remaining.

Radioactive Dating:Radioactive Dating: a method to determine age of objects a method to determine age of objects compares amount of parent isotope to compares amount of parent isotope to

daughter isotope.daughter isotope.

Example: Carbon dating measure the Example: Carbon dating measure the ratio of carbon-12 and carbon-14.ratio of carbon-12 and carbon-14.– Stable carbon-12 and radioactive carbon-Stable carbon-12 and radioactive carbon-

14 exist naturally in a constant ratio.14 exist naturally in a constant ratio. In nature, carbon-12 appears 98.9% of the In nature, carbon-12 appears 98.9% of the

time, while carbon-14 is very rare.time, while carbon-14 is very rare.

When an organism dies, carbon-14 stops When an organism dies, carbon-14 stops being taken in and continues to slowly being taken in and continues to slowly decay.decay.– Comparing the amounts of carbon-12 to Comparing the amounts of carbon-12 to

carbon-14 is called carbon-14 is called radiocarbon datingradiocarbon dating and and gives us an age for the object.gives us an age for the object.

– Radiocarbon dating only works for organisms Radiocarbon dating only works for organisms less than 50,000 years old because the half-life less than 50,000 years old because the half-life of carbon-14 is 5730 years. (after 50,000 of carbon-14 is 5730 years. (after 50,000 years, there isn’t enough C-14 left!)years, there isn’t enough C-14 left!)

There are many radioisotopes There are many radioisotopes that can be used for datingthat can be used for dating

some elements require one step to decay, some elements require one step to decay, while others decay over many steps while others decay over many steps before reaching a stable daughter isotope.before reaching a stable daughter isotope.– Carbon-14 decays into nitrogen-14 in one stepCarbon-14 decays into nitrogen-14 in one step– Uranium-235 decays into lead-207 in fifteen Uranium-235 decays into lead-207 in fifteen

steps.steps.– Thorium-235 decays into lead-208 in ten Thorium-235 decays into lead-208 in ten

steps.steps.

The Potassium-40 ClockThe Potassium-40 Clock Radioisotopes with very long half-Radioisotopes with very long half-

lives can help determine the age of lives can help determine the age of very old things.very old things. The potassium-40/argon-The potassium-40/argon-40 clock has a half-life of 40 clock has a half-life of 1.3 billion years.1.3 billion years.

Argon-40 produced by the Argon-40 produced by the decay of potassium-40 decay of potassium-40 becomes trapped in rock.becomes trapped in rock.

Ratio of potassium-40 : Ratio of potassium-40 : argon-40 shows age of argon-40 shows age of rock.rock.

Half-life ProblemsHalf-life Problems::

1. What mass of a 200g sample of 1. What mass of a 200g sample of carbon-14 remains after 22,920 carbon-14 remains after 22,920 years?years?

2. A rock has 420g of radioactive 2. A rock has 420g of radioactive isotope. What percentage would isotope. What percentage would remain after 5 half-lives?remain after 5 half-lives?