The half-life of a radioactive substance is 1 | vedclass

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(A) Given: Half-life $T_{1/2} = 100 \ s$. Total time $t = 5 \ min = 5 	imes 60 \ s = 300 \ s$. Initial amount $N_0 = 8 \ g$. The number of half-lives

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$1$

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(A) Given: Half-life $T_{1/2} = 100 \ s$. Total time $t = 5 \ min = 5 	imes 60 \ s = 300 \ s$. Initial amount $N_0 = 8 \ g$. The number of half-lives $n$ is given by $n = \frac{t}{T_{1/2}} = \frac{300}{100} = 3$. The remaining amount $N$ is given by the formula $N = N_0 	imes (1/2)^n$. Substituting the values: $N = 8 	imes (1/2)^3 = 8 	imes (1/8) = 1 \ g$. Therefore,$1 \ g$ of the substance will remain.

The half-life of a radioactive substance is $100 \ s$. How many grams of the radioactive substance will remain after $5 \ min$ if the initial amount is $8 \ g$ (in $g$)?

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