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Q.

The isotopes U238 and U235 occur in nature in the mass ratio 140:1. It is assumed that initially they were found in equal mass. If half life (t½) of U238 = 4.5 × 109 and t½ of U235 = 5 × 108 year respectively, then the age of earth in years is (log 7 = 0.846; log 2 = 0.3)

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a

4.02 × 109

b

2.01 × 109

c

8.72 × 109

d

None of these

answer is A.

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Detailed Solution

For U238;K1t=ln⁡n0n1  For U235;K2t=ln⁡n0′n2. K1−K2t=ln⁡n0n1×n2n0′ ln⁡210.5×109−14.5×109t=ln⁡(140)t=4.02×109 year
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