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: Calculate 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 initial amount and decay rate

The initial amount $I = 100$ grams. For a half - life situation, the decay rate $r=\frac{1}{2}$.

Step3: Use the decay formula

The formula for remaining amount is $A = I(1 - r)^n$. Substituting $I = 100$, $r=\frac{1}{2}$, and $n = 6$ into the formula, we get $A=100\times(1-\frac{1}{2})^6$.
$A = 100\times(\frac{1}{2})^6=100\times\frac{1}{64}=\frac{100}{64}=\frac{25}{16}=1.5625$ grams.

Answer:

$1.5625$ grams