Question

the half - life of strontium - 90 is approximately 29 years. how much of a 500 g sample of strontium - 90 will remain after 58 years? remaining amount = ?(1 - )^ remaining amount = i(1 - r)^t

Explanation:

Step1: Identify initial amount, decay rate and number of half - lives

The initial amount $I = 500$ g. The decay rate $r=\frac{1}{2}$ for each half - life. The number of half - lives $t=\frac{58}{29}=2$.

Step2: Substitute values into the formula

The formula for remaining amount is $Remaining\ Amount = I(1 - r)^t$. Substitute $I = 500$, $r=\frac{1}{2}$ and $t = 2$ into it. We get $Remaining\ Amount=500\times(1-\frac{1}{2})^2$.

Step3: Calculate the result

First, calculate $1-\frac{1}{2}=\frac{1}{2}$. Then $(\frac{1}{2})^2=\frac{1}{4}$. So $500\times\frac{1}{4}=125$ g.

Answer:

125 g