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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2×109 years

4×109 years

6×109 years

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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