The half-life of a radioactive element is 12. | vedclass

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(B) The formula for radioactive decay is given by $M = M_{0} \left(\frac{1}{2}\right)^{n}$,where $n = \frac{t}{T_{1/2}}$ is the number of half-lives.G

Vedclass · Accepted Answer

$100$

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(B) The formula for radioactive decay is given by $M = M_{0} \left(\frac{1}{2}ight)^{n}$,where $n = \frac{t}{T_{1/2}}$ is the number of half-lives.Given: $M = 1 \; g$,$M_{0} = 256 \; g$,and $T_{1/2} = 12.5 \; h$.Substituting the values: $1 = 256 \left(\frac{1}{2}ight)^{n}$.This simplifies to $\frac{1}{256} = \left(\frac{1}{2}ight)^{n}$.Since $256 = 2^{8}$,we have $\left(\frac{1}{2}ight)^{8} = \left(\frac{1}{2}ight)^{n}$.Therefore,$n = 8$.Using $n = \frac{t}{T_{1/2}}$,we get $t = n 	imes T_{1/2} = 8 	imes 12.5 \; h = 100 \; h$.

The half-life of a radioactive element is $12.5 \; h$ and its initial quantity is $256 \; g$. After how much time (in $h$) will its quantity remain $1 \; g$?

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