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InterviewSolution
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A factory produces a radioactive substance A at a constant rate R which decays with a decay constant ` lmabda` to form a stable substance. Find (a) the number of nuclei of A and (b) number of nuclei of B, at any time t assuming the production of A starts at `t=0`. (c ) Also, find out the maximum number of nuclei of `A` present at any time during its formation. |
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Answer» Factory `underset(const.rate)overset(R) rarr A underset(decay)overset(lambda) rarrB` Let `N` be the number of nuclei of A any time t. `because (dN)/(dt)=R-lambdaN" "underset(0)overset(N)(int)(dN)/(R-lambdaN)=underset(0)overset(t)(int)dt` On solving, we will get `N = R//lambda (1-e^(-lambda t))` (b) Number of nuclei of B at any tiem t, `N_(B) =Rt -N_(A)` `=R t-R//lambda(1-e^(-lambda t) )=R//lambda(lambda t -1 +e^(- lambda t))` Maximum number of nuclei of 'A' present at any time during its formation ` =R//lambda` . |
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