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Question

40K isotope of potassium has a half life of 1.37×109 years and decays to an isotope of argon which is stable. In a particular sample of moon rock, the ratio of potassium atoms to argon atoms was found to be 1:7. The age of the rock, assuming that originally there was no argon present, is

A
4.11×109 years
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B
2.74×109 years
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C
5.48×109 years
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D
1.37×109 years
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Solution

The correct option is A 4.11×109 years
Given that, T1/2=1.37×109 years

At present,

Number of K atomsNumber of Ar atoms=17

As there were no argon present initially, so

Number of K atoms present initially = number of K atoms + number of Ar atoms present now.

Let,

Number of K-atoms present nowNumber of K-atom present initially=NN0

NN0=11+7=18

Let age of rock be n half-lives of Knuclide. Then,

NN0=(12)n

18=(12)n

n=3

Therefore, the age of the rock is,

t=nT1/2

t=3×1.37×109

t=4.11×109 years

Hence, option (A) is correct.

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