Question

the half - life of a particular radioactive substance is 10 seconds. if you started with 100 grams of this substance, how much of it would remain after 60 seconds? remaining amount =? (1 - ) remaining amount = i(1 - r)^t

Explanation:

Step1: Determine the number of half - lives

The half - life is 10 seconds and the total time is 60 seconds. So the number of half - lives $n=\frac{60}{10}=6$.

Step2: Identify the initial amount and decay factor

The initial amount $I = 100$ grams. For radioactive decay with half - life, the decay factor $r=\frac{1}{2}$ in the formula $A = I(1 - r)^n$.

Step3: Calculate the remaining amount

Substitute $I = 100$, $r=\frac{1}{2}$, and $n = 6$ into the formula $A=I(1 - r)^n$. So $A = 100\times(1-\frac{1}{2})^6$.
$A = 100\times(\frac{1}{2})^6=100\times\frac{1}{64}=\frac{100}{64} = 1.5625$ grams.

Answer:

$1.5625$ grams