1.

If alpha=2N_0lambda, calculate the number of nuclei of A after one half-life of A, and also the limiting value of N as

Answer»

`2N_0, 5/2N_0`
`3N_0, 2N_0`
`4N_0, 2N_0`
`3/2N_0, 2N_0`

Solution :If `ALPHA=2lambdaN_0`, t=half LIFE =` (In(2))/lambda`
`therefore N=1/lambda[2lambdaN_0-(2lambdaN_0-lambdaN_0)e^(-lambdat)]`
or `N=(lambdaN_0)/lambda[2-e^(In(2))][Here""e^(-In(2))=2^(-1) = 1/2]`
or `N=(lambdaN_0)/lambda[2-1/2] =(3N_0)/2 ` or `N=3/2N_0`
When `t to oo ` and `alpha = 2lambdaN_0`
`N=alpha/lambda=(2lambdaN_0)/lambda=2N_0` or `N=2N_0`


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