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Q.

Half lives of two isopotes X and Y of an element are known to be 2×109  years and  4×109 years respectively. If a planet was formed with equal number of these isotopes atoms, estimate the current age of the planet, given that currently the planet has 20% of X and 80% of Y by number.

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a

2×109 years

b

4×109 years

c

6×109 years

d

8×109 years

answer is D.

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Detailed Solution

NX=N02e−λ1t     ......(i)NY=N02e−λ2t       .......(ii) Dividing (ii) by (i) eλ1−λ2t=4⇒λ1−λ2t=ln⁡4⇒ln⁡210912−14t=2ln⁡2⇒t=8×109 years
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