Carbon-14 Radioactive Dating

 stable nitrogen in atmosphere + cosmic ray particle   à   electron capture takes place

reaction #1:        nitrogen-14  +  electron capture  -->  carbon-14

carbon in atmosphere forms  CO₂       13 % is carbon-14       87% is carbon-12

all living things take in CO₂ till death  à upon death carbon-14 starts to decay (beta decay) at regular rate to stable nitrogen-14

 reaction #2:     carbon-14  -->  beta particle  +  nitrogen-14

 

Half-life:
t_1/2  =  average length of time needed for 1/2 the mass of radioactive sample to decay into a different substance

1 half-life for carbon-14 is 5730 years.

carbon-14 dating technique is useful for organic materials up to 50 000 years old (about 10 half-lives)

 technique has been checked by tree rings (chronodendrology) and super novas

technical name for process is neutron induced decay

calculations:

amount radioactive remaining  =  original amount
                                                                      2ⁿ                     n = number of half-lives

 Problems:

Given 2.40 grams of a radioactive substance, calculate the amount of original radioactive sample remaining and the amount of material decay after 6 half-lives. 

Given 400. grams of a radioactive substance, calculate the number of half-lives that would have to pass for only approximately 10 grams to remain radioactive.