Assume that two radioactive substances A and B disintegrate as:
`(-d[A])/(dt) = k_(A), t_(1//2)(A) = 0.693/(K_(A))`
`(-d[B])/(dt) = k_(B)[B]^(2), t_(1//2)(B) =1/(k_(B)[B]_(0)]`
If both the half life periods and initial concentrations are equal, what will be the ratio of the rates of the two substances at the start of the reaction?

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1 Answers

According to available data, `t_(1//2)(A) = t_(1//2)(B)`
`0.693/k_(A) = 1/(k_(B)[B]_(0))` or `k_(A)/k_(B)= 0.693[B]_(0)= 0.693[A]_(0)`
At the start of the reaction
`r_(A) = k_(A)[A]_(0)`, `r_(B) = k_(B)[B]_(0)^(2) = k_(B)[A]_(0)^(2)` ……......`[therefore[A]_(0) = [B]_(0)]`
`therefore r_(A)/r_(B) = (k_(A)[A]_(0))/(k_(B)[A]_(0)^(2))` or `r_(A)/r_(B) = 0.693 [A]_(0) xx ([A]_(0))/([A]_(0^(2))) = 0.693`

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