Question

Use Table 1: Analysis of Decay in the laboratory guide to answer this question: Scientists find a piece of wood that is thought to be from an ancient fire circle. They find that the wood contains an amount of carbon-14 (14C) that is approximately 1/16 of the current atmospheric 14C levels. Determine approximately how many years ago the tree was chopped down to be used for the firewood. If you started with 1 million carbon-14 atoms, how many atoms would remain in the wood? 14C has a t1/2 of 5,750 years.
Why is 14C dating a good method to use for dating a human leg bone but not so good a method for dating a dinosaur bone? You may have to check the dates of the existence of humans and dinosaurs on earth on a chart showing the geological eras.
Potassium-40 (40K) is a radioactive material that decays into argon-40 (40Ar). The half-life of a sample of 40K is 1.3 billion years. Rocks containing 40K have been around since the formation of the earth, and 40Ar gas has been accumulating in those rocks since the earth formed. However, when rocks are heated by volcanic action, all the 40Ar leaves the rock when the gases escape. Create a scenario and discuss, based on your knowledge of half-life, the value of potassium-argon dating to geologists.

Answer 1

1/2=5750 years, 1/2(1/2)=1/4, (1/2)(1/2)(1/2)=1/8, (1/2)(1/2)(1/2)(1/2)=1/6
4 halflives have passed so 4(5750)=23000 years since the tree was chopped down
1000000 atoms (1/2)=500000 atoms(1/2)=250000(1/2)=125000(1/2)=62500 atoms would remain in the wood after 4 halflives
Dinosaurs became extinct around 62 million years ago, so if 14C's half life has a value of 5750 years, it would be gone or in such small amounts that dating would be ineffective today.
As Potassium decays into Argon in 1.3 billion years, apart from volcanic activity, it would enable geologists to effectively date things that are really, really, really old.