Suppose you are trying to date a rock using the Potassium-Argon method, which is

Question

Suppose you are trying to date a rock using the Potassium-Argon method, which is based upon the decay of Potassium-40 into Argon-40, a process which, as you can see from the familiar chart at the bottom right of this page, has a half-life of 1.25 billion years. Suppose that in the rock you measure the amounts of those two isotopes and find that there are twice as many Argon-40 atoms in the rock as Potassium-40 atoms. In other words, the relative percentages of the two are in the ratio of 66% to 33% (which is two to one), which is to say that the "% of parent isotope remaining" (that's the parameter on the vertical axis of the graph) is just 33%. Use the radiative decay graph in your Study Packet to estimate the age of the rock. ___ How old is the rock if the % of Potassium-40 parent isotope remaining is 80%?__

Explanation / Answer

18.

Ar-40/K-40 = 2

1/2 = 0.5

number of half lives required to reach 0.5

(1/2)^n = 0.5

n log(0.5) = log(0.5)

n = 1

age pf rock = 1.25 x 10^9 yr

19. If K-40 was 80%

Ar-40/K-40 = 2/8 = 0.25

number of half lives required to reach 0.5

(1/2)^n = 0.25

n log(0.25) = log(0.5)

n = 2

age pf rock = 2 x 1.25 x 10^9 yr = 2.5 x 10^9 yr

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