If there is 0.1 mg of radioactive Th^{234}, | vedclass

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(C) The formula for radioactive decay is given by $N = N_0 \left( \frac{1}{2} \right)^{t/T}$, where $N_0$ is the initial amount, $t$ is the total time

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$3.125$

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(C) The formula for radioactive decay is given by $N = N_0 \left( \frac{1}{2} ight)^{t/T}$, where $N_0$ is the initial amount, $t$ is the total time, and $T$ is the half-life.Given: $N_0 = 0.1 \ mg = 100 \ \mu g$, $t = 120 \ 	ext{days}$, and $T = 24 \ 	ext{days}$.The number of half-lives elapsed is $n = \frac{t}{T} = \frac{120}{24} = 5$.Substituting the values into the formula:$N = 100 	imes \left( \frac{1}{2} ight)^5 = \frac{100}{32} \ \mu g$.$N = 3.125 \ \mu g$.Thus, the remaining amount of undecayed substance is $3.125 \ \mu g$.

If there is $0.1 \ mg$ of radioactive $Th^{234}$, how much of it will remain undecayed after $120 \ \text{days}$, given its half-life is $24 \ \text{days}$? (Answer in $\mu g$)

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