Module 8
1. Module 8
1.11. Page 2
Module 8—Nuclear Decay, Energy, and the Standard Model of the Atom
Explore
Half Life
The half-life of a radioactive isotope is defined as the amount of time it takes for half of the radioactive particles to decay. Consider a container with 128 unstable nuclei. Over time, some of the nuclei decay, forming daughter nuclei and related decay particles. Eventually, half of the nuclei will have decayed into daughter nuclei. In this example, after a certain amount of time had passed, 64 nuclei decayed to daughter nuclei, leaving 64 of the original parent nuclei.
The amount of time it takes for this to happen is defined as the half-life of the unstable parent nuclei. The half-life of other nuclei will be different. For example carbon-14, which is used to date organic material, has a half-life of 5730 years. While iodine-131, used in the medical diagnosis of thyroid problems, has a half-life of 192 hours.
Think About It
With such a short half-life, any iodine-131 found today was not around when Earth was formed.
Module 8: Lesson 2 Assignment
Remember to submit the answer to LAB 1, LAB 2, LAB 3, LAB 4, LAB 5, LAB 6, and LAB 7 to your teacher as part of your Module 8: Lesson 2 Assignment.
A simulation will be used to explore the rate of radioactive decay and the concept of half-life. Open the Half-life simulation. Use the controls on the right side of the simulation to activate the animation.
LAB 1. In the simulation there is a chamber of 128 radioactive atoms represented by red spheres. Click Play (
) and observe. Over time, describe what happens to the relative amount of parent nuclei (red) and daughter nuclei (grey).
LAB 2. Reset the simulation and select the “BAR CHART” tab. Click play and observe. Compare the rate of change from parent to daughter nuclei throughout the decay process. Is the rate of particle decay constant through time? If not, did it speed up or slow down over time?
LAB 3. Reset the simulation and select the “GRAPH” tab. Click play and observe. Sketch the half-life curve. (You can find a blank graph, like the one that follows, in your Module 8: Lesson 2 Assignment.)
LAB 4. Select a different isotope from the drop-down menu and observe its decay graph. Does it have exactly the same shape as the other isotope decay curve? What does this suggest about the nature of decay?
LAB 5. The rate of decay of a radioactive isotope is described by its half-life. On the simulation, ensure that the half-life is set to 20 seconds and select “Theoretical decay” from the second drop-down menu. Check that the initial number of atoms is 128. Select the “TABLE” tab and click play.
- At 20 seconds, how many of the original 128 radioactive atoms remained?
- How many remained at 40 seconds? 60 seconds? 80 seconds? 100 seconds? What is the pattern?
LAB 6. If there are 100 radioactive atoms with a half-life of 30 seconds, how many radioactive atoms will remain after one half-life (30 seconds)? How many will remain after two half-lives (60 seconds)? three half-lives? Use the simulation to check your answers.
LAB 7. The half-life of a radioactive isotope is defined as the amount of time it takes for half of the radioactive particles to decay. Start with 128 particles and a half-life of 30 seconds. (“Theoretical decay” should still be selected.) Select the “GRAPH” tab and click play. Turn on the half-life probe and ensure it is on the y-axis of the graph. (You can "grab" and drag the probe by clicking on one of the purple triangles or the line between.)
- What is the time value and number of radioactive particles at the beginning of the interval measured by the probe? What is the time value and number of radioactive particles at the end of this interval? How are these two numbers related to the definition of half-life?
- Drag the probe to different parts of the graph. Does the same pattern persist?
The mathematical expression for the graph of parent nuclei versus time gives the following equation for determining the number of original parent nuclei in a radioactive sample after a given time interval. |
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Activity is usually measured in decays per second, or becquerels (Bq); however, mass and percentages can also be used to indicate the relative amount of parent material. Since these units appear on both sides of the equation, they will mathematically cancel one another.
Graphical representation of radioactive decay.
The half-life can be measured from the time axis from the point where half of the nuclei have transmuted. In this case, 50 nuclei are left after 25 seconds. |
Example Problem 1. A radioactive sample has an activity of 3.2 × 103 Bq. The isotopes in the sample have a half-life of 24 hrs. What will be the activity of this sample after five days have passed?
Given
Required
the amount of activity after five days
Analysis and Solution
Determine the number of half-lives that have elapsed.
Determine the amount remaining.
Paraphrase
After five days, the sample will have an activity of 1.0 × 102 Bq.