The activity of a radioactive sample is 6000 | vedclass

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(D) The activity of the radioactive sample decreases from $6000 \, dps$ to $3000 \, dps$ in $140$ days.Since the activity becomes half of its value,th

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$24000$

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(D) The activity of the radioactive sample decreases from $6000 \, dps$ to $3000 \, dps$ in $140$ days.Since the activity becomes half of its value,the half-life $(T_{1/2})$ of the sample is $140$ days.The time elapsed from the start to the first measurement is $280$ days.Number of half-lives $(n)$ $= \frac{280}{140} = 2$.Let the initial activity be $A_0$. The activity $A$ after $n$ half-lives is given by $A = A_0 	imes (1/2)^n$.Given $A = 6000 \, dps$ at $n = 2$,we have $6000 = A_0 	imes (1/2)^2$.$6000 = A_0 	imes (1/4)$.$A_0 = 6000 	imes 4 = 24000 \, dps$.

The activity of a radioactive sample is $6000 \, dps$ after $280$ days. After another $140$ days,the activity decreases to $3000 \, dps$. The initial activity of the radioactive sample (in $dps$) is ........

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