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In moon rock sample the ratio of the number of stable argon-40 atoms present to the number of radioactive potassium-40 atoms is 7:1. Assume that all the argon atoms were produced by the decay of potassium atoms, with a half-life of 2.5 × 109 yr. The age of the rock is

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a

2.5 109 yr

b

5.0 109 yr

c

7.5 109 yr

d

1010 yr

answer is C.

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Detailed Solution

At present ; No. of arg on atomsNo. of K atoms=71∴No. of K atomsTotal No. of atoms=11+7=18=123∴NN0=123=12t/T ; ∴3=t/Tt=3T=3 x 2.5 x109 ; ∴t=7.5 x 109 yr
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In moon rock sample the ratio of the number of stable argon-40 atoms present to the number of radioactive potassium-40 atoms is 7:1. Assume that all the argon atoms were produced by the decay of potassium atoms, with a half-life of 2.5 × 109 yr. The age of the rock is