Question

chapter 17 homework
conceptual checkpoint 17.4 - enhanced - with feedback

graph: x-axis time (years) from 0 to 600, y-axis mol nuclide from 0 to 0.12, red curve decreasing

part a
what is the half-life of the nuclide?

options:
○ 50 yrs
○ 100 yrs
○ 250 yrs
○ 500 yrs

Explanation:

Step1: Understand Half - Life Concept

Half - life is the time it takes for half of a radioactive substance (nuclide, in this case) to decay. So we start with the initial amount of the nuclide. From the graph, at time \(t = 0\) years, the amount of nuclide is \(0.10\) mol (since the \(y\) - axis is mol nuclide and at \(x = 0\), the \(y\) - value is \(0.10\)).

Step2: Find Time for Half Decay

We need to find the time when the amount of nuclide is half of the initial amount. Half of \(0.10\) mol is \(0.05\) mol. Now we look at the graph to find the time when the \(y\) - value (mol nuclide) is \(0.05\) mol. From the graph, when the amount of nuclide is \(0.05\) mol (close to \(0.05\), maybe a slight approximation due to the graph's grid), the corresponding \(x\) - value (time) is \(100\) years. Let's verify:

• Initial amount (\(N_0\)): \(0.10\) mol.
• After \(t = 100\) years, the amount \(N\) is around \(0.05\) mol (from the graph, at \(x = 100\), the \(y\) - value is approximately \(0.05\) mol). Since \(N=\frac{N_0}{2}\) when \(t = t_{1/2}\) (half - life), and \(\frac{0.10}{2}=0.05\) at \(t = 100\) years, this means the half - life is \(100\) years.

Answer:

100 yrs (corresponding to the option "100 yrs")