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Lead is the final product formed by a se...

Lead is the final product formed by a series of changes in which the rate determining stage is the radioactive decay of uranium -238 with a half life of `4.5 times 10^9 yr`. What would be the age of a rock sample originally lead free in which the molar proportion of uranium to lead is now `1:3`

A

a)`1.5 times 10^9 yr`

B

b)`2.25 times 10^9 yr`

C

c)`4.5 times 10^8 yr`

D

d)`9.0 times 10^9 yr`

Text Solution

Verified by Experts

The correct Answer is:
D
All radioactive processes follor first order kinetics. Intially sample is free from lead. If its proportion is x , the amount of sample at time T is 4x.
`implies 0.693/(4.5 times 10^9 yr)=2.303/Tlog""(4x)/x`
`T= 2 times 4.5 times 10^9 yr =9.0 times 10^9 yr`
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