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The decay constant of a radioactive subs...

The decay constant of a radioactive substance is `lambda`.At t=0 , the number of active nuclei are `N_0`. Select the correct alternatives

A

The number of nuclel decayed in time internal `0-t'` is `N_(0)e^(-lambdat)`

B

The number of nuclel decayed in time internal `0-t'` is `N_(0)(1-e^(-lambdat))`

C

The probability that a radioactive nuclel does not decay I inteval `0-t` is `e^(-lambdat)`

D

The probability that a radioactive nuclel does not decay I inteval `1-e^(-lambdat)`

Text Solution

Verified by Experts

The correct Answer is:
B, C
At `t = 0, N_(1) = N_(0)`
At time `t : N_(2) = N_(0)e^(-lambdat)`
Decayed in time `t (N_(1) - N_(2)) = N_(0)(1-e^(-lambdat))`
Porbability that a radioactive nuclei does not decay in `t = 0` to `t : (N)/(N_(0)) = (N_(0)e^(-lambdat))/(N_(0)) = e^(-lambdat)`
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Knowledge Check

  • The decay constant of a radioactive isotope is lambda . If A_1 and A_2 are its activites at time t_1 and t_2 respectively, then the number of nuclei which have decayed the time (t_1-t_2)

    A
    `A_1t_1-A_2t_2`
    B
    `A_1-A_2`
    C
    `(A_1-A_2)//lambda`
    D
    `lambda(A_1-A_2)`

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