Transcript of Radiometric Dating

[music] 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 ½ of the original parent radioactive   material to decay into daughter product. For example: Carbon-14 decays to Nitrogen-14   with a half-life of 5700 years. The numbers—14 –  indicate particular isotopes 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 number of neutrons, istotopes).  Carbon-14 is a carbon isotope with 6 protons   and 8 neutrons (total 14). Carbon-12 is a  carbon isotope with 6 protons and 6 neutrons   (total 12). Carbon-13 is a carbon isotope  with 6 protons and 7 neutrons (total 13).   Pause now. [music] Any naturally occurring substance with carbon in it will have about 99% Carbon-12, 1.1% 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 CaCO3) 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 5700 years, ½ 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 1:1 – equal. After two half-lives,   the ½ that remained of parent after the first half  life is now halved again. Half of a half is ¼.   The remaining ¾ is daughter, and the ratio of  Parent to Daughter is 1:3. Another half-life,   and we halve the ¼. There’s now 1/8 parent and  7/8 daughter, and the ratio is 1:7 and so on.   At this point, 3 half-lives have passed, and the  time is 5700 x 3 or 17,100 years. A shell that   was buried 17,100 years ago would have a Carbon  -14/Nitrogen-14 ratio of 1:7. 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. [music] 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. Fortunately,   there are a number of other pairs such as:  Uranium-238 which decays to Lead-206 and has   a half life 4.5 billion years, Uranium -235 which  decays to Lead-207 and has a half-life 700 million   years, Potassium-40 which decays to Argon-40  and has 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. [music] So how do we date a meteorite? First,   we ensure 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 we’re  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, ½ 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 U-238 to Pb 206! That ratio of 1:1 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 Lead-207 to date the same   meteorite? What would we find as 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 6.7 half-lives. Let’s look at what  that means for the ratio. One half life gives a   ratio of ½ parent to ½ daughter or 1:1. Two half  lives halve the parent again so we have a ratio of   ¼ parent to ¾ daughter or 1:3. Three half lives  = 1/8:7/8 or 1:7. Four half-lives = 1/16:15/16   or 1:15. Five half-lives = 1/32:31/32 or 1:31.  Six half lives = 1/64:63:64 or a ratio of 1:63.   And Seven half lives = 1/128 parent to 127/128  daughter or 1:127. So the ratio we’d expect for   something that had experienced 6.7 half-lives is  somewhere close to 1:127, close to 7 half-lives.   To be more precise, we use this equation: the  fraction of parent remaining = e to the power of   (-T/1.443), where T is the number of half lives  passed. Since T is 6.7, that means the fraction   of parent remaining is 0.00963. The remaining  0.99037 must be daughter. And the ratio is 1:103.   Calculating age using multiple isotope pairs  is a method we use to confirm our dates.   Pause now. [music] For more information and more detail, continue on to the next video in this series. [music]