The half-life of a radioactive element is 100 | vedclass

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(C) For a radioactive decay (first-order kinetics),the time taken for $50\%$ decay is $t_{50\%} = 1 	imes t_{1/2} = 100 \, 	ext{min}$.For $87.5\%$ d

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$200$

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(C) For a radioactive decay (first-order kinetics),the time taken for $50\%$ decay is $t_{50\%} = 1 	imes t_{1/2} = 100 \, 	ext{min}$.For $87.5\%$ decay,the remaining amount is $100\% - 87.5\% = 12.5\%$.Since $12.5\% = (1/2)^3$,this corresponds to $3$ half-lives.Thus,$t_{87.5\%} = 3 	imes t_{1/2} = 3 	imes 100 = 300 \, 	ext{min}$.The time interval between these two stages is $\Delta t = t_{87.5\%} - t_{50\%} = 300 \, 	ext{min} - 100 \, 	ext{min} = 200 \, 	ext{min}$.

The half-life of a radioactive element is $100 \, \text{min}$. The time interval between the stages of $50\%$ and $87.5\%$ decay will be ...... $\text{min}$.

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