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Updated on : 2022-09-05

Solution

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Correct option is A)

For sample 1 we can write,

$N_{1}=N_{o}_{1}e_{−λ_{1}t}$

$N_{2}=N_{o}_{2}e_{−λ_{2}t}$

Given that at a particular time t $N_{1}=2N_{2}$

Also given that

For sample 1,

$A_{1}=−dtdN_{1} =N_{o}_{1}λ_{1}e_{−λ_{1}t}=5μC_{i}$

$A_{2}=−dtdN_{2} =N_{o}_{2}λ_{2}e_{−λ_{2}t}=10μC_{i}$

Solvong above equations we get,

$λ_{2}λ_{1} =41 $

$halflife_{2}halflife_{1} =λ_{1}ln2 ×ln2λ_{2} =4$

$T_{S_{1}}=4T_{S_{2}}$

$⇒T_{S_{1}}=20$ years and $T_{S_{2}}=5$ years is the possible answer.

$⇒T_{S_{1}}=20$ years and $T_{S_{2}}=5$ years is the possible answer.

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