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Question

The isotopes U238 and U235 occur in nature in the ratio 140 : 1. Assuming that at the time of earth formation, they were present in equal ratio, the estimated age of the age of earth will be :
(The half-life period of U238 and U235 are 4.5×109 and 7.13×108 years, respectively.)

A
6.04×109 years
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B
6.25×109 years
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C
6.59×109 years
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D
non of these
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Solution

The correct option is A 6.04×109 years
In nature, NU238NU235=1401 (at t = t)
At the time of earth formation.
N0U238N0U235×NU235NU238=1140

For U238,N0U238N0U235=eλ238t .... (1)

For U235,N0U238NU235=eλ235t .... (2)

N0U238N0U235×NU235NU238=e(λ238λ235)t

1140=e(λ238λ235)t

e(λ238λ235)t=loge1loge140

[0.6934.5×1090.6937.13×108]t=2.303log140
=4.9416
t=6.04×109 years

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