A radioactive substance has a half-life of 60 | vedclass

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Question

(B) The number of atoms remaining after time $t$ is given by $N = N_0 \left( \frac{1}{2} \right)^{\frac{t}{T_{1/2}}}$.Given,half-life $T_{1/2} = 60\,

Vedclass · Accepted Answer

$87.5$

Vedclass · Answer

(B) The number of atoms remaining after time $t$ is given by $N = N_0 \left( \frac{1}{2} ight)^{\frac{t}{T_{1/2}}}$.Given,half-life $T_{1/2} = 60\, minutes = 1\, hour$.Total time $t = 3\, hours$.The number of half-lives $n = \frac{t}{T_{1/2}} = \frac{3}{1} = 3$.The fraction of atoms remaining is $\frac{N}{N_0} = \left( \frac{1}{2} ight)^3 = \frac{1}{8}$.The fraction of atoms that have decayed is $1 - \frac{N}{N_0} = 1 - \frac{1}{8} = \frac{7}{8}$.In percentage,this is $\frac{7}{8} 	imes 100 = 87.5\%$.

$A$ radioactive substance has a half-life of $60\, minutes$. After $3\, hours$,the fraction of atoms that have decayed would be ......... $\%$

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