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There are three lumps of a given active substance. Their activities are in the ratio of $1 : 2 : 3$ now. What will be the ratio of their activities at any further date?

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Solution

Suppose the activities of the lumps at present are $A_{1}, A_{2} and A_{3} .$
$A_{1} : A_{2} : A_{3} = λ N_{1} : λ N_{2} : λ N_{3} = 1 : 2 : 3 .$
After time t, Let their activities be $A_{1}^{1}, A_{2}^{1} and A_{3}^{1}$
$\begin{array}{l} ∴ A_{1}^{1} : A_{2}^{1} : A_{3}^{1} = {λN}_{1}^{1} : {λN}_{2}^{1} : {λN}_{3}^{1} = N {}_{1}e^{- λt} : N {}_{2}e^{- λt} : N {}_{3}e^{- λt} \\ = 1 : 2 : 3 . \end{array}$

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Radio activity

Remember concepts with our Masterclasses.

There are three lumps of a given active substance. Their activities are in the ratio of 1 : 2 : 3 now. What will be the ratio of their activities at any further date?

Suppose the activities of the lumps at present are A1, A2 and A3. A1: A2 : A3=λ N1:λ N2:λ N3=1:2:3. After time t, Let their activities be A11 ,A21 and A31 ∴ A11 :A21: A31=λN11: λN21: λN31=Ne −λt 1 : Ne −λt 2 :Ne −λt 3 =1:2:3.

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There are three lumps of a given active substance. Their activities are in the ratio of $1 : 2 : 3$ now. What will be the ratio of their activities at any further date?