The half-life of a radioactive element is 30 | vedclass

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(C) Given: Half-life $T_{1/2} = 30$ days,Total time $t = 90$ days.Number of half-lives $n = \frac{t}{T_{1/2}} = \frac{90}{30} = 3$.The remaining amoun

Vedclass · Accepted Answer

$87.5$

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(C) Given: Half-life $T_{1/2} = 30$ days,Total time $t = 90$ days.Number of half-lives $n = \frac{t}{T_{1/2}} = \frac{90}{30} = 3$.The remaining amount of the radioactive substance is given by $N = N_0 \left(\frac{1}{2}ight)^n$.Substituting the values: $N = N_0 \left(\frac{1}{2}ight)^3 = \frac{N_0}{8}$.The amount that has decayed is $N_{decayed} = N_0 - N = N_0 - \frac{N_0}{8} = \frac{7N_0}{8}$.The percentage of decay is $\frac{N_{decayed}}{N_0} 	imes 100 = \frac{7}{8} 	imes 100 = 87.5\%$.

The half-life of a radioactive element is $30$ days. What percentage of the element will have decayed in $90$ days?

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