# Carbon dating and half life

*11-Jun-2020 05:01*

Understand how decay and half life work to enable radiometric dating.Play a game that tests your ability to match the percentage of the dating element that remains to the age of the object.A useful concept is half-life (symbol is \(t_\)), which is the time required for half of the starting material to change or decay.Half-lives can be calculated from measurements on the change in mass of a nuclide and the time it takes to occur.For example, if there were \(100 \: \text\) of \(\ce\)-251 in a sample at some time, after 800 years, there would be \(50 \: \text\) of \(\ce\)-251 remaining and after another 800 years (1600 years total), there would only be \(25 \: \text\) remaining.Remember, the half-life is the time it takes for half of your sample, no matter how much you have, to remain.Each half-life will follow the same general pattern as \(\ce\)-251.The only difference is the length of time it takes for half of a sample to decay.

(\(\ce\)-240 has a half-life of 1 hour) Solution \[\text = \dfrac (60 \, \text) \nonumber\] After 4 hours, only \(3.75 \: \text\) of our original \(60 \: \text\) sample would remain the radioactive isotope \(\ce\)-240.\[720\cancel\times \dfrac= 30\, days \nonumber\] \[n=3 =\dfrac \nonumber\] \[\text = \dfrac (8.0 \, ug) \nonumber\] After 720 hours, 1.0 ug of the material remains as \(\ce\)-225 .