Warm up: The half life of a particular element is 10 days. Answer the following questions using that information. How many days will have passed after 4 half-lives? If my sample starts off with 100 grams of the element, how many grams will be remaining after 4 half-lives? After 4 half-lives, what fraction of the original sample remains?

Half-life and decay

Half- life The half-life of a radioactive isotope is the amount of time it takes ½ of a radioactive substance to decay into a new isotope. Do not be misled! That does not mean that in two half-life periods the entire substance has decayed.

Half-life Every half-life period that goes by means that another half of the sample has decayed. EXAMPLE A radioactive isotope has a half-life of 10yrs. How much of a 100g sample will remain after 20yrs. has passed? In 10yrs. ½ will decay that leaves 50g. In the next 10yrs. ½ of the 50g remaining will decay. That leaves 25g after 20yrs.

Practice a few on you own Carbon – 14 has a half-life of 5,715yrs. How much of a 43g sample will remain after 17,145yrs. have passed. 5.375g A sample of Strontium-90 is found to have decayed to one-eighth of its original amount after 87.3 years. What is the half-life of strontium-90? 29yrs.

Using the formula for half-life The formula for half-life exponential decay is: 𝑦=𝑎 1 2 𝑥 y – the remaining amount of the sample a – the original amount of the sample x – the half-life period

Half-life and dating objects This rate of decay is constant and can be used to date objects. If you know the rate of decay then you can compare the amount of a known sample to the amount of its decay product to determine the age. One isotope does not work in all cases. The most well known is probably carbon-14 dating. Because the half-life of carbon-14 is relatively short this method of dating is only usable if a sample is less than 50,000yrs. Old.

Half-life and dating objects For over 50,000yrs. old other methods of dating need to be used such as uranium/lead dating or potassium/argon dating. Accuracy of these methods depends on several factors. Amount of the sample available for analysis Amount of the sample collected from several locations No contamination has occurred. As long as the above conditions have been met most radiometric dating techniques have a %error under 10%