The technique known as potassium-argon dating is used to date old lava flows. Th

Question

The technique known as potassium-argon dating is used to date old lava flows. The potassium isotope^40K has a 1.28 billion year half-life and is naturally present at very low levels.^40K decays by two routes: 89% undergo beta-minus decay into^40Ca while 11% undergo electron capture to become^40Ar. Argon is a gas, and there is no argon in flowing lava because the gas escapes. Once the lava solidifies, any argon produced in the decay of 40K is trapped inside and cannot escape. A geologist brings you a piece of solidified lava in which you find the^40Ar/^40K ratio to be 1.9 times 10^-2. What is the age of the rock? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

T1/2 ( K- 40) = 1280000000 years

lamda = 0.693/T1/2 = 0.693/1280000000 years = 5.414 * 10^-10 years^-1

Ar/K = 0.019

Ar+ lamda /lamda = 0.019(5.414 * 10^-10 years^-1) + ( 5.414 * 10^-10 years^-1/ 5.414 * 10^-10 years^-1 = 1.019 = No/N

N = No exp ^-lamda t

1/1.019 = exp^-lamdaT

lamda T = 0.0188

T = 0.0188/lamda = 0.0188/5.414 * 10^-10 years^-1 = 0.0348 billion years

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