1.

The mean lives of an unstable nucleus in two different decay processes are 1620 yr and 405 yr, respectively. Find out the time during which three-fourth of a sample will decay.

Answer» Correct Answer - D
Let at some instant of time t, number of nuclei are N. Then,
`((-dN)/(dt))_(net)=((-dN)/(dt))_1+((-dN)/(dt))_2`
If the effective decay constant is `lambda`, then
`lambdaN=Lambda_1N+lambda_2N`
or `lambda=lamba_1+lambda_2=1/1620+1/405=1/324year^-1`
Now, `N_0/4=N_0e^(-lambdat)`
:. `-lambdat=1n(1/4)=-1.386`
or `(1/324)t=1.386`
:. `t=449 yr`


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