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2-iodo butane (having radioactive iodine) reacts with KI (having non radioactive iodine). Rate of loss of optical activity was 1.96 times the rate of loss of radioactivity. What percentage of reaction proceeds via SN1 mechanism? Assume that 100% inversion takes place in SN2 reaction while in SN1 there is 50% retention and 50% inversion.

I proceeded with KI substituting the iodide ion with the radioactive iodide ion but couldn't understand how would 2-iodo butane lose its optical activity(it still has a chiral C). So I couldn't go any further.

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It has to do with an (equimolar) Racemic mixture being formed! Note that a racemic mixture still has chiral atoms but cannot contribute to any net rotation of the plane polarized light making it optically inactive as a combined product

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