Physics 248, Spring 2009 Lab 6: Radiation and its Interaction with Matter

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1 Name Section Physics 48, Spring 009 Lab 6: Radiation and its Interaction with Matter Your TA will use this sheet to score your lab. It is to be turned in at the end of lab. To receive full credit you must use complete sentences and explain your reasoning clearly. In this lab, you will use a Geiger counter to investigate the radiation from two radioactive sources, 60 Co (cobalt-60) and 04 Tl (thallium-04). Their properties are: Particle emitted Particle energy Half-life 60 Co Photon (γ) 1.3 MeV 5.3 years 04 Tl Electron (β) Max 0.75 MeV 3.8 years You will measure the penetrating power of the radiation from these sources through different thicknesses of aluminum and lead for 60 Co, and through plastic for 04 Tl. Since the measurement procedures are all the same, your lab group will investigate only one combination of source and absorber. You will then record the other groups data, so you will have data for all different source/absorber combinations. We will be doing only section MPC-1b of the MPC-1 lab in the lab manual. Your TA will distribute radioactive source(s) to your group. If you will work with a 04 Tl β emitter (plastic (poly) absorber), your TA will remove the plastic cap from your Geiger counter (the electrons can t penetrate through much at all). Groups using the 60 Co source (Al or Pb absorber) should leave the caps on to protect the very thin and fragile detector window from the γ radiation. The groups are as follows: Group 1: One 60 Co source in slot #5 (from top). [two lab tables] Group : Two 60 Co sources on top of each other in the bottom slot. [two tables] Group 3: One 04 Tl source in slot #5 with the writing side down. [the rest of the lab tables] 1) Go to the web version of the lab manual and click on the Launch NC-1B icon to start up the PASCO software.

2 ) Turn on your Geiger counter by plugging it into input 1 of the PASCO interface. Make sure any radioactive sources are at least 1 m away. The Geiger counter should click periodically, as it detects cosmic rays and other background radiation. Take data with the PASCO interface for 300 seconds (it will stop automatically). What is the background count rate (average counts / second)? 3) Put the appropriate number of sources on the clear tray, and slide the tray in the appropriate slot (see above). Make sure the side without writing faces the detector. Determine the mean number of decays/second (don t forget to subtract the background signal). There are 10 sec in each data sample. 4) Radioactive decay is a random process; the decay of any individual nucleus cannot be predicted. In each time interval dt an individual nucleus has the same fixed probability rdt of decaying, where r is the decay rate of an individual nucleus (also called the decay constant). The number of nuclei that decay in a given time interval is proportional to the number of nuclei N in the sample and the probability that an individual nucleus decays. Think of this as rolling a die once per second trying to get a six, which here means decayed. Each roll tells you whether the nucleus decayed in that dt of 1 second. Each time you roll, you have the same 16.7% chance to get a six, so the decay rate r is 0.167/s. For radioactive nuclei, the decay rate is much smaller, which you can think of as rolling a cup of many dice once per second, trying to get all sixes each time. a. Keeping in mind that the number of particles decreases with time, write down the differential equation that governs the number of nuclei that decay per unit time (dn/dt), and solve it to obtain N(t), given that at t=0, N(t)=N 0.

3 b. The decay constant r is related to the mean lifetime, τ by r=1/ τ. In nuclear physics, usually the half-life t 1/, and not the decay rate or the mean lifetime, is specified for the material. The half-life t 1/ = ln() / r = ln()!. Use the listed half-life to calculate the decay rate (in sec -1 ) and mean lifetime (in sec) of a single nucleus for your source. c. When you roll N dice, there are 6 N possible ways for them to come up, but only one of these is all sixes. About how many dice would you have to roll once per second to make the rate of getting all sixes the same as your radioactive source decay rate? d. The number of decays per second you measured in part 3) are only a fraction of the total number of decays. First, the radiation goes in all directions, but the detector intercepts a fraction of it, given by!r window /4!r sample (here r window =4.6mm is the detector window radius and r sample is the distance of the source(s) from the detector window). Second, the detector only has an efficiency of 10%. Use your results from part 3 to find the number of radioactive nuclei in your source. 3

4 5) You will now determine how well different materials can stop radiation. Your group will do only one source/absorber combination, then combine data with other groups. Group 1: Two 60 Co sources on top of each other in slot #5 (from top). Use 0, 1,, and 3 lead absorbers (each 0.5 thick). Group : Four 60 Co sources on top of each other in the very bottom slot. Use 0,, 4, and 6 aluminum absorbers Group 3: Two 04 Tl sources on top of each other in slot #5 (writing side down). Use 0, 1, and 3 D poly absorbers (each thick). (Remove the plastic Geiger counter protective cap.) a) Put your results in the table. Answer b) and c) below while data accumulates. Source Absorber Thickness in cm ( T ) None 0 Counts / sec Counts / sec - background b) Your counts/sec will go down as you add more absorbers. As an example, suppose that each absorber absorbs 50% of the radiation hitting it. For 0, 1,, and 3 total absorbers, make a bar chart of what you would expect for the transmitted radiation. Fraction getting through Number absorbers c) As you saw in b), your counts / second C go down exponentially with the absorber thickness T as C( T) = C o e!"t. What is the meaning of the constant α? Will α depend on the material? The source? 4

5 d) Take the ln of both sides of C( T) = C o e!"t to show that the ln(count rate) is linear in the thickness T. Determine α in units of cm -1 for your source/absorber combination by plotting ln(count rate) v. T. e) Using all groups data, summarize α for different source/absorber combinations. Source Particle emitted Absorber α (cm -1 ) What general conclusions can you draw about the penetrating power of photons vs electrons? About the stopping power of aluminum vs lead? What is the explanation? 5