Part #1: Potassium-40 is used to date rocks that are millions to billions of yea

Question

Part #1:

Potassium-40 is used to date rocks that are millions to billions of years old. A rock initially contains 1.62*10-11 grams of potassium-40 (molar mass = 39.96 g/mol). How many atoms of Potassium-40 are in the sample?

Part #2:

Potassium-40 has a half-life of 1.210 * 109 years. What is the rate constant k in years-1?

Part #3:

How many atoms in the initial sample of Potassium-40 should decay in one year?

Part #4:

Several geologic ages have passed, and the rock now has 2.135 x 1011 atoms of Potassium-40 that decay in a year. How old is the rock in years?

Explanation / Answer

1.

No of K-40 atoms = ((1.62*10^(-11))/40)*6.023*10^23

   = 243931500000 atoms

2. K = 0.693/T1/2

k = (0.693/(1.21*10^9)) = 5.73*10^-10 y-1

3.

5.73*10^-10 = (1/1)ln(243931500000/x)

No of atoms decay in one year = 243931500000 - 243931499860

   = 140 atoms

4.

5.73*10^-10 = (1/t)ln(243931500000/(2.135*10^11))

t = 2.325*10^8 years

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