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Question

In a sample of radioactive material what fraction of the initial number of active nuclei will remain undisintigrated after half life of the sample?
1) 1/4. 2) 1/2 3) 1/21/2 4) 1

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Solution

The explanation is as follows.

Half-life (symbol t1⁄2) is the time required for a quantity(here the number of active nucei) to reduce to half its initial value. The term is commonly used in to describe how quickly unstable atoms undergo, or how long stable atoms survive, radioactive decay.
So by this definition it is clear that after one half life the half of initial active nucei remains undisintegrated.
So answer is option (2),1/2.

Hope it answers your question.
All the best!

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