The half-life of a radioactive substance is 3 | vedclass

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(D) The formula for the remaining mass of a radioactive substance is given by $M = M_0 \left( \frac{1}{2} \right)^{\frac{t}{T_{1/2}}}$.Here, the initi

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$0.019$

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(D) The formula for the remaining mass of a radioactive substance is given by $M = M_0 \left( \frac{1}{2} ight)^{\frac{t}{T_{1/2}}}$.Here, the initial mass $M_0 = 20\, mg$, the total time $t = 36\, days$, and the half-life $T_{1/2} = 3.6\, days$.The number of half-lives $n = \frac{t}{T_{1/2}} = \frac{36}{3.6} = 10$.Substituting these values into the formula:$M = 20 	imes \left( \frac{1}{2} ight)^{10}$.$M = 20 	imes \frac{1}{1024}$.$M = 0.01953125\, mg$.Rounding to three decimal places, we get $M \approx 0.019\, mg$.

The half-life of a radioactive substance is $3.6$ days. How much of $20\, mg$ of this radioactive substance will remain after $36$ days?

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