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The decay constant of a radioactive spec...

The decay constant of a radioactive species is `lambda` for the process in which a parent element showing formation of a daughter element.After time t, P atoms of parent element ar left and D atoms of daughter elements are formed. If `t_(1//2)` is half life then which expression correctly represents decay of parent element,

A

`t = (t_(1//2))/(0.693)` In `(1 + (D)/(P))`

B

`t = (t_(1//2))/(0.693)` In `(1 -(D)/(P))`

C

`t = (t_(1//2))/(0.693)` In `((D)/(P))`

D

`t = (t_(1//2))/(0.693)` In `((P)/(D))`

Text Solution

Verified by Experts

The correct Answer is:
A
For P to D, `t = (1)/(lambda) "1n" (N_(0))/(N), " "N_(0) = P + D, N = P, t = (1)/(lambda)`
`"1n" [(P + D)/(P)] = (t_(1//2))/(0.693) "1n" [1 + (D)/(P)]`
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