The disintegration rate of a certain radioactive sample at any instant is 4750 dpm (disintegration per minute). Five minutes later, the rate becomes 2700 dpm. Calculate half-life of sample.
A
6.1328 min
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B
9.3328 min
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C
7.2328 min
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D
None of these
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Solution
The correct option is A 6.1328 min −dNdt=λN0 at start −dNdt=λN0 after time t 4750=λN0 2700=λN ∴N0N=47502700 Also λ=2.3035logN0N =2.3035log4750200=0.113min−1 ∴t50=0.693λ=0.6930.113=6.1328min