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=ln4⇒ln210912−14t=2ln2⇒t=8×109 years