A radioactive material of half-life 2.5 hours | vedclass

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(D) The activity of a radioactive sample at time $t$ is given by $A = A_0 (1/2)^n$, where $n = t/T_{1/2}$ is the number of half-lives.Given that the i

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$12.5$

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(D) The activity of a radioactive sample at time $t$ is given by $A = A_0 (1/2)^n$, where $n = t/T_{1/2}$ is the number of half-lives.Given that the initial activity $A_0 = 32 A_{safe}$ and we want the final activity $A = A_{safe}$.Substituting these into the formula: $A_{safe} = 32 A_{safe} 	imes (1/2)^n$.Dividing both sides by $A_{safe}$, we get $1 = 32 	imes (1/2)^n$, which simplifies to $(1/2)^n = 1/32$.Since $32 = 2^5$, we have $(1/2)^n = (1/2)^5$, which implies $n = 5$.Since $n = t/T_{1/2}$, we have $5 = t / 2.5$.Therefore, $t = 5 	imes 2.5 = 12.5 	ext{ hours}$.

$A$ radioactive material of half-life $2.5$ hours emits radiation that is $32$ times the safe maximum level. The time (in hours) after which the material can be handled safely is

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