A radioactive substance is being consumed at a constant of `1 s^(-1)`. After what time will the number of radioactive nuclei becoem `100`. Initially, there were 200 nuceli present.A. `1 s`B. `(1)/(1 n(2))s`C. `ln(2)s`D. `2s`

A radioactive substance is being consumed at a constant of `1 s^(-1)`.

1.	A radioactive substance is being consumed at a constant of `1 s^(-1)`. After what time will the number of radioactive nuclei becoem `100`. Initially, there were 200 nuceli present.A. `1 s`B. `(1)/(1 n(2))s`C. `ln(2)s`D. `2s`
Answer» Correct Answer - c Let N be the number of nuclei at any time t. Then, `(dN)/(dt) =200 -lambda N` `:.int_(0)^(N) (dN)/((200 -lambda N)) = int_(0)^(t)dt` or N=(200)/(lambda) (1-e^(-lambda t))` Given: `N =100 and lambda =1 s^(-1)` `:. 100=200 (1-e^(-t))` or `e^(-t)=((1)/(2)) :. t=In(2) s`.

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A radioactive substance is being consumed at a constant of `1 s^(-1)`. After what time will the number of radioactive nuclei becoem `100`. Initially, there were 200 nuceli present.A. `1 s`B. `(1)/(1 n(2))s`C. `ln(2)s`D. `2s`

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