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Q.

The radioactivity of a sample is $A_{1}$ at time $t_{1} and A_{2}$ at time $t_{2}$ . If the mean life of the specimen is T, the number of atoms that have disintegrated in the time interval of $(t_{2} - t_{1})$ is:

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a

$(A_{1} - A_{2})$

b

$\frac{(A_{1} - A_{2})}{T}$

c

$(A_{1} - A_{2}) T$

d

$A_{1} t_{1} - A_{2} t_{2}$

answer is C.

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Detailed Solution

$A_{1} = N_{1} λ, A_{2} = N_{2} λ Mean life, T = \frac{1}{λ}$

$A_{1} - A_{2} = (N_{1} - N_{2}) λ = (N_{1} - N_{2}) \frac{1}{T}$

So, number of atoms disintegrated in

$(t_{2} - t_{1}) \sec = (N_{1} - N_{2}) = (A_{1} - A_{2}) T$

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