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 initial amount, decay rate and number of half - lives

The initial amount $I = 100$ grams. The decay rate $r$ for a half - life situation is $r=\frac{1}{2}$. The half - life is 10 seconds and the time elapsed $t = 60$ seconds, so the number of half - lives $n=\frac{60}{10}=6$.

Step2: Use the decay formula

The formula for radioactive decay is $A = I(1 - r)^n$. Substituting $I = 100$, $r=\frac{1}{2}$ and $n = 6$ into the formula, we get $A=100\times(1-\frac{1}{2})^6$.

Step3: Calculate the remaining amount

First, calculate $(1-\frac{1}{2})^6=(\frac{1}{2})^6=\frac{1}{64}$. Then, $A = 100\times\frac{1}{64}=\frac{100}{64}=\frac{25}{16}=1.5625$ grams.

Answer:

$1.5625$ grams