The probability that a randomly chosen nucleus in a radioactive sample will have decayed in a given time is 96.875%. The sample has experienced 5 half lives. The correct option is A.
What is half life?
Half life is the time required for the heavy nucleus or any radioactive material to disintegrate by half its quantity.
After one half life, the probability of decay of any nucleus is given by 50%. = 0.5
After two half lives gone, probability of decay is 0.5 + 1/2(0.5) = 0.75
After, three half lives gone, probability of decay is 0.5 + 1/2(0.5) + (1/2)²(0.5) = 0.875
After, four half lives gone, probability of decay is 0.5 + 1/2(0.5) = 0.875 + (1/2)³(0.5) = 0.9375.
After, five half lives gone, probability of decay is 0.9375 + (1/2)⁴(0.5) = 0.96875.
Thus, the sample has experienced 5 half lives. The correct option is A.\
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