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Question

A freshly made radioactive sample gives a count rate of 8000 counts per minute. After twenty days, it gives a count-rate of 500 counts per minute. What is the half-life of the material?

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Solution

lnAoAt=ktln(8000500)=k×20ln16=k×20k=ln1620=ln(2)420k=4ln220k=ln25t1/2=ln2k=ln2ln2×5t1/2=5days

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