The radioactivity of a sample is R1 at time T1 and R2 at time T2 . If the half life of the specimen is T, number of atoms that have disintegrated in time (T2−T1) is proportional to
A
(R1T1−R2T2)
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B
(R2−R1)T
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C
(R2−R1)T
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D
(R1−R2)(T1−T2)
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Solution
The correct option is B(R2−R1)T Radioactivity =−dNdt=λN (since N(t)=N0e−λt) Given: R1=λN(T1) R2=λN(T2) Number of disintegrated atoms =N(T2)−N(T1) =R2−R1λ =(R2−R1)Tln 2