how do we determine the age of a rock a shell or a meteorite radiometric dating first step we need to identify a radioactive parent material that is present in our rock and that decays into daughter material at a rate that ensures enough of both parent and daughter in the rock to measure them there are a number of parent daughter radioactive decay pairs and each pair has a different decay rate known as a half-life half-life is the amount of time it takes for one half of the original parent radioactive material to decay into daughter product for example carbon-14 decays to nitrogen-14 with a half-life of 5730 n-- indicate a particular isotope of these atoms for example all atoms with 6 protons are carbon atoms all nitrogen atoms have 7 protons however each atom can have varying amounts of neutrons and we call all those permutations the same atom but different numbers of neutrons isotopes carbon-14 is a carbon isotope with six protons and eight neutrons total 14 carbon-12 is a carbon isotope with six protons and six neutrons total 12 carbon 13 is a carbon isotope with six protons and seven neutrons total 13 pause now any naturally occurring substance with carbon in it will have about 99% carbon-12 1.1 percent carbon 13 and some trace amounts of the radioactive carbon-14 isotopes what makes carbon 14 and nitrogen 14 a very good isotope pair is that most substances that contain carbon in a structure such as shells made of calcium carbonate do not also have nitrogen in them so any nitrogen 14 we see in the material will have come from the decay process for carbon-14 every 5,700 years half of the original carbon-14 has decayed to nitrogen 14 after one half-life assuming there was no nitrogen 14 to begin with in a rock sample the ratio of the two should be one to one equal after two half-lives the half that remained if parent after the first half-life is now hafta get 1/2 of 1/2 is 1/4 the remaining 3/4 is daughter and the ratio of parent to daughter is 1 to 3 another half-life and we have the quarter there's now one eighth parent and 7/8 daughter and the ratio is one to seven and so on at this point three half-lives have passed and the time is 5,700 times 3 or 17 thousand 100 years a shell that was buried 17,000 100 years ago would have a carbon-14 nitrogen-14 ratio of 1 to 7 if we are trying to use the carbon-14 nitrogen 14 radioactive decay pair to date a rock that's 100 million years old there likely will not be enough parent left to measure and that would not be a good choice pause now in addition to the carbon-14 nitrogen-14 pair being useful only for relatively young rocks this pair is also useful only if there is carbon in the rock and specifically carbon that was present in a living organism at some point on Earth's surface while one half of all meteorites do contain some carbon they fail on the other two requirements and so we need to identify another radioactive decay pair to date meteorites fortunately there are a number of other pairs such as uranium 238 which decays to lead 206 and has a half-life of 4.5 billion years uranium 235 which decays to lead 207 and has a half-life of 700 million years potassium-40 which decays to argon-40 and as a half-life of 1.4 billion years second step we need to ensure the rock or shell or bone fragment has remained a closed system while parent decays into daughter there must be no migration of parent or daughter isotopes into or out of the rock otherwise the ratios we see do not reflect decay over the lifetime of the rock for example if a rock has undergone extensive metamorphism at high heats atoms become mobile within the rock and can migrate in and out similarly if a rock undergoes chemical weathering on its surface minerals can break down and atoms can migrate in and out pause now so how do we date a meteorite first we insure it was a closed system by picking a good sample without any weathering or evidence of melting then we place a sample of it in a mass spectrometer to measure the ratio of the particular radioactive decay pair were studying in this case uranium 238 and lead-206 when asteroids first coalesce they contain plenty of uranium 238 but no lead-206 the only way to produce lead 206 is as a radioactive decay daughter product of uranium 238 every 4.5 billion years 1/2 of uranium 238 will decay into lead 206 so if we open a closed system asteroid that formed 4.6 billion years ago with no lead 206 at that time and no loss or gain from or to the outside world since we can use the ratio of the parent and daughter within to determine how long decay has been happening or how old the meteorite is and what do we find almost exactly equal amounts of uranium 238 to lead 206 that ratio of 1 to 1 is possible only if exactly one half-life has passed the meteorite formed about 4.5 billion years ago of course in the lab we get a lot more precise what if we used uranium 235 and led 207 to date the same meteorite what would we find is our ratio remember the half-life for uranium 235 to lead 207 is 700 million years for something that is 4.6 billion years old that means it would have passed through six point seven half-lives let's look at what that means for the ratio one half-life gives a ratio of 1/2 parent to 1/2 daughter or 1/2 1/2 half-lives have the parent again so we have a ratio of 1/4 parent to 3/4 daughter or one two three three half-lives one eighth to seven eighths or one two seven four half-lives 1/16 to fifteen sixteenths or 1 to 15 five half-lives one thirty-second to 31 30 seconds or one to thirty one six half-lives one over 60 four to 63 over 64 or a ratio of one to 63 and seven half lives is one over a hundred and twenty-eight parent to 127 128 s daughter or one to 127 so the ratio we'd expect for something that had experienced six point seven half lives is somewhere close to one 227 close to seven half lives to be more precise we use this equation the fraction of parent remaining equals e to the power of minus T divided by one point four four three where T is the number of half-lives passed since T is six point seven that means the fraction of parent remaining is zero point zero zero nine six three the remaining point nine nine zero three seven must be daughter and the ratio is one to 103 calculating age using multiple radioactive isotope pairs is a method we use to confirm our dates pause now for more information and more detail continue on to the next video in this series