K 40 isotope of potassium has a half life of 1.37 x10 9 years & decays to an iso

Question

K40 isotope of potassium has a half life of 1.37 x109 years & decays to an isotope of Argon which isstable. In a particular sample of moon rock, the ratio of K atomsto Ar atoms was found to be 1:7 . Estimate the age of the rock,assuming that originally there was no argon present
1. 4.11 x 109 years 2. 2.74 x 109 years 3. 5.48 x 109 years 4. 1.37 x 109 years K40 isotope of potassium has a half life of 1.37 x109 years & decays to an isotope of Argon which isstable. In a particular sample of moon rock, the ratio of K atomsto Ar atoms was found to be 1:7 . Estimate the age of the rock,assuming that originally there was no argon present
1. 4.11 x 109 years 2. 2.74 x 109 years 3. 5.48 x 109 years 4. 1.37 x 109 years

Explanation / Answer

In general the decay is expressed as N(t)=N0 e -t/ = 1.37 x 109 years and For time t the amount of K40 is N(t)= 1/8 of theoriginal N0 then we have 1/8 = 1 e -t/1.37 x109     then t= - 1.37 x 109 ln(1/8 ) t= 2.84 x 109 years I would go with b) I would go with b)

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