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.

Question

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.

Infinity Learn · Accepted Answer

$$NX=N02e$$−λ$$1t$$     ......(i)NY=N02e$$−λ$$2t$$       .......$$(ii) Dividing (ii) by (i) eλ$$1$$−λ$$2t=4$$⇒λ$$1$$−λ$$2t=ln$$⁡$$4$$⇒ln⁡$$210912$$−$$14t=2ln$$⁡$$2$$⇒$$t=8$$×$$109$$ years

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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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