1RadioactivityPHYS 1301 F99Prof. T.E. Coanversion: 6 Aug ‘98IntroductionThis lab will simulate the behavior of a radioactive material, such as a clumpof carbon-14 nuclei. Radioactivity is the spontaneous decay or transformation of anucleus containing some number of protons into another nucleus containing adifferent number of protons. The number of protons may either increase or decrease.This process is spontaneous in the sense that you don’t have to do anything to theradioactive nucleus in order for this transformation to occur. You do not have to shinelight on the nucleus, heat it, hit it, apply pressure to it or anything else. As a result ofthis transformation, particles are emitted from the nucleus. These particles are eitherelectrons, anti-electrons (called positrons), helium nuclei (called alpha particles) andphotons of high energy (so-called gamma rays). These photons have too high anenergy, and hence too small a wavelength, for your eye to detect them.Radioactivity is surprisingly common in nature. For example, carbon-14, anisotope of carbon whose nuclei contain 6 protons and 8 neutrons versus the 6 protonsand 6 neutrons of the more common carbon-12 isotope, occurs in nature at a relativeconcentration of about 1 part in a billion compared to that of carbon-12. Although thismay sound like a miniscule abundance, carbon-14 is a practical tool for dating the ageof many formerly living objects. It is also the case that at least one common household device relies onradioactivity for its operation. Most smoke detectors in houses, apartments andschools have a quantity of the radioactive element Americium in them. The nuclei in aparticular isotope of this element (so-called Americium-241) undergo radioactivedecay and emit helium nuclei in the process. These helium nuclei ionize thesurrounding air and the positively and negatively charged ions drift towardsoppositely charged electrodes of the smoke detector and produce an electrical current.When this electrical current is stopped or reduced because of the presence of smokebetween the electrodes of the smoke detector, the smoke detector’s electronic circuitrysounds an obnoxious buzzer you sometimes hear.The rate at which radioactive nuclei decay is often summarized by the notionof its “half-life.” A half-life is the amount of time it takes for one-half of an arbitraryamount of radioactive material to radioactively decay. The half-life of a givenradioactive material is constant, although the exact time at which a particularradioactive nucleus will decay is random. (An event is said to be random when youcannot predict it.) Although this seems weird, there is no contradiction here. Thenotion of a half-life is a probabilistic one and applies to the behavior of a largecollection of radioactive nuclei. Strictly speaking, you cannot meaningfully speak ofthe half-life of a single radioactive nucleus because when the decays, all of it decaysand not just half of it. This probabilistic nature of radioactivity makes it a uniquelyquantum mechanical phenomenon.2Procedure1. Locate the folder PEARLS. The instructor will help you if you can’t find it.Double click (left mouse button) on it. Inside, locate the folder Modern Physics,click on it and continue until you have launched the RADIOACTIVITY module.2. You first need to understand the display. Click GO and watch the display. Theradioactive nuclei will change color when they have decayed. The program willautomatically keep track of the number of remaining radioactive nuclei and theelapsed time. Make sure you can find these numbers See the instructor if youcannot.3. Set the initial population of radioactive nuclei to 500. Set the initial half-life to 10seconds. Set the time zoom to the value 1. 4. Question 1. I want you to fill out Table 1. You will start and stop the display in 2second intervals, recording the number of surviving nuclei at the end of eachinterval N. You do not need to stop at exactly 2 second intervals, just come asclose as you can. You might want to practice a bit before you start for real.Continue recording numbers until the elapsed time equals 36 seconds or so.Question 2. Plot the number of surviving nuclei versus time. (Yes, this means youneed to find some graph paper.) Do your data points fall on a straight line? Dothey fall on a curve?5. Again set the initial population of radioactive nuclei to 500. Set the half-life to 2seconds. Set the time zoom to 0.1. This will slow down the apparent rate at whichthe nuclei will decay, allowing you to more easily record numbers.6. Question 3. I want you now to fill out Table 2. To do this, you will need to startand stop the display in consecutive 2-second intervals. This means you will startthe simulation and record the number of radioactive nuclei at the start of theinterval N0, and then stop the simulation after 2 seconds have elapsed. You willthen record the number of surviving radioactive nuclei N. This number ofsurviving nuclei will then become the starting number of nuclei for the next 2second interval, and so on. Question 4. What is your average value for NN0? Becareful to exclude from your average fractions where N=0. Is your averageconsistent with the half-life you had programmed the simulation with? Is youraverage exactly equal to the half-life you programmed the simulation with? Whatdo you make of this?7. Again set the initial population of radioactive nuclei to 500. Set the half-life to 10seconds. Set the time zoom to 1.0.8. Question 5. I want you to fill out Table 3. For each of the initial populations inthe table, I want you to run the simulation for just 1 second and then record thenumber of surviving nuclei N. Fill out the last column as well. This last column isthe number of nuclei that decayed in 1 second and is a kind of average of theactivity of the radioactive substance or the total number of radioactive decays persecond. The activity is not a property of a particular radioactive nucleus. Question36. Plot the number of decayed nuclei versus the starting population N0. (If N=0you can stop collecting data.) Draw a smooth curve through these data points.(Smooth means smooth. The curve should not look like the stock market report.)Question 7. Can you form a conclusion about the activity of a radioactivesubstance and the size of the starting population?4RadioactivityPHYS1301 F99Prof. T.E. CoanName: ___________________________ Section: ________________Abstract:QuestionsQuestion 2:Question 4:Question