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>>Introduction to Radioactivity
>> $A freshly made radioactive sample gives$

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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Updated on : 2022-09-05

Solution

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$ln \frac{A _{o}}{A _{t}} = k t ln (\frac{8 0 0 0}{5 0 0}) = k \times 20 ln 16 = k \times 20 k = \frac{ln 1 6}{2 0} = \frac{ln ( 2 ) ^{4}}{2 0} k = \frac{4 ln 2}{2 0} k = \frac{ln 2}{5} t_{1 / 2} = \frac{ln 2}{k} = \frac{ln 2}{ln 2} \times 5 t_{1 / 2} = 5 d a y s$

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