Chapter 11: Problem 13

After four half-lives, about how much radioactive parent material is left?

Short Answer

Expert verified

After four half-lives, approximately \(6.25\%\) of the radioactive parent material will remain.

Step by step solution

Identify the given information

Here, we are given that after four half-lives have passed, we need to find the percentage of radioactive parent material remaining. Number of half-lives (n) = 4

Use the exponential decay formula to calculate the amount remaining

Use the formula for exponential decay: \(Amount\ Remaining = Initial\ Amount\ (1/2)^n\) Since we want to find the percentage of radioactive parent material remaining: \(Percentage\ Remaining = (Amount\ Remaining / Initial\ Amount) * 100\) As we are not given the initial amount, we can denote it as \(P_0\). Considering that we want a percentage, we will divide the \(Amount\ Remaining\) by the initial amount, which will cancel the \(P_0\) from the equation: \(Percentage\ Remaining = \frac{P_0 * (1/2)^n}{P_0} * 100\) Simplifying the equation: \(Percentage\ Remaining = (1/2)^n * 100\)

Plug in the given number of half-lives and solve

With the number of half-lives (n) = 4, the equation becomes: \(Percentage\ Remaining = (1/2)^4 * 100\) Calculating the remaining percentage: \(Percentage\ Remaining = (1/16) * 100\) Multiply to get the remaining percentage: Percentage Remaining ≈ 6.25% After four half-lives, approximately 6.25% of the radioactive parent material will remain.

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After four half-lives, about how much radioactive parent material is left?

Short Answer

Step by step solution

Identify the given information

Use the exponential decay formula to calculate the amount remaining

Plug in the given number of half-lives and solve

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