the radioistotope potassium-40 decays to argon-40 by positron emission with a half life of 1.3 x 10^9 yr.?

Question

A sample of moon rock was found to contain 78 argon-40 atoms for every 22 potassium-40 atoms. The age of the rock is...

a. 8.1 x 10^[-]10 yr
b. 2.4 x 10^9 yr
c. 2.8 x 10^9 yr
d. 4.6 x 10^9 yr
e. 6.8 x 10^9 yr

&& How do you answer/breakdown a sort of question like this? (((THANK YOU))).

Answer 1

78 Ar-40 atoms and 22 K-40 atoms means you have a sample containing 100 atoms total.

The problem says that K-40 is your reactant in the nuclear decay and Ar-40 is your product. We will use how much K-40 is left over to determine how many half lives have taken place.

100 atoms K-40 left ~> 0 half lives.
50 atoms K-40 left ~> 1 half life.
25 atoms K-40 left ~> 2 half lives.
between 12 and 13 atoms K-40 left ~> 3 half lives.

So, if there are 22 K-40 atoms left, between 2 and 3 half lives have taken place.

Since 1 half life = 1.3x10^9 years, 2 half lives = 2.6x10^9 years and 3 half lives = 3.9x10^9 years.

So, you are looking for a number of years between the 2 and 3 half life marks. The only choice in that range is C.

Answer 2

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