# The age of wine can be determined by measuring the trace amount of radioactive tritium. Tritium is formed by cosmic bombardment in the upper atmosphere, so naturally occurring water contains a small amount of the isotope. Once the water is in the bottle, the tritium diminishes by a first order radioactive decay with a half-life of 12.5 years. If a bottle of wine was found to have a tritium concentration that is 0.1000 that of freshly bottled wine, what is the age of the wine?

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The age of wine can be determined by measuring the trace amount of radioactive tritium. Tritium is formed by cosmic bombardment in the upper atmosphere, so naturally occurring water contains a small amount of the isotope. Once the water is in the bottle, the tritium diminishes by a first order radioactive decay with a half-life of 12.5 years. If a bottle of wine was found to have a tritium concentration that is 0.1000 that of freshly bottled wine, what is the age of the wine?

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Step 1

Radioactive decay follows first order kinetics. Tritium is a radioactive isotope of hydrogen and follows first order kinetics.

In first order kinetics, the reaction time is proportional to the logarithm of ratio of initial amount of radioactive isotope to that of amount remaining at present.

Half life is the time at which half of the radioactive isotope  has decayed.

Step 2

As per question, the amount of tritium present is 0.1000 that of freshly bottled wine, it means the amount of tritium at present is 0.1000 of its initial amount.

The age of wine can be calculated using the integrated rate law equation for first order  which is given as

Step 3

As the rate constant is not provided, it can be calculated using half life...

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