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To determine the half life of a radioact...

To determine the half life of a radioactive element , a student plote a graph of in `|(dN(t))/(dt)| versus t , Here |(dN(t))/(dt)|` is the rate of radioatuion decay at time t , if the number of radoactive nuclei of this element decreases by a factor of p after `4.16 ` year the value of p is

Text Solution

Verified by Experts

The correct Answer is:
8
`N =N_0 e^(-lambda t)`
`ln|dN|dt|=1n(N_0 lambda)-lambda t`
From graph
`lambda =(1)/(2)` per year
`(t_(1))/(2)=(0.693)/(1//2)=1.386` year
`4.16` years `=3t_(1//2)`
`p=8`.
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Knowledge Check

  • Nuclei of a radioactive element A are being produced at a constant rate alpha . The element has a decay constant lambda . At time t=0, there are N_0 nuclei of the element . The number N of nuclei of A at time t is

    A
    `1/lambda[alpha + (alpha -N_0lambda)e^(-lambdat)]`
    B
    `1/lambda[alpha - (alpha -N_0lambda)e^(-lambdat)]`
    C
    `lambda[alpha - (alpha -N_0lambda)e^(-lambdat)]`
    D
    `[alpha-(N_0lambda-alpha ) e^(-lambdat)]`