Experiment #54 Absorption and Backscattering of β-rays References 1. B. Brown, Experimental Nucleonics 2. I. Kaplan, Nuclear Physics 3. E. Segre, Experimental Nuclear Physics 4. R.D. Evans, The Atomic Nucleus Introduction β-particles are high energy electrons. They are scattered principally by the electrons (both free and bound) in matter, hence the absorption of β-rays will depend on the total electron density, which in turn is proportional to the mass density of the material. For example, 1 mm of lead absorbs β-rays to approximately the same extent as 4 mm of aluminum. In this experiment, you will investigate the absorption and backscattering of β-particles by aluminum. Absorption If an object is placed between a β-source and a Geiger counter, the counting rate will be reduced due to absorption of some of the β-rays by the object; the amount will depend on the thickness of the object. A typical curve of count rate as a function of thickness is shown in Figure 1. log(n β ) 0 z Figure 1: Typical log-linear plot of count rate N β as a function of absorber thickness z for β-rays. Deviation from exponential form are expected at small and large thicknesses.
The tail of the curve is due to γ-rays produced by the β-rays during scattering in the absorber. The absorber thickness at which the two portions of the curve intersect is called the range of the β-rays. As may be expected, the range depends on the energy of the incident β-radiation. Backscattering A small fraction of the β particles incident on a surface are not absorbed or transmitted, but scattered backwards. This process, called backscattering, is due to β-particles going around a nucleus, rather like a comet orbiting the sun. The Geiger-Müller Counter Radioactive particles can be detected by making use of the different ways in which they interact with matter. This experiment will demonstrate the principles and use of the Geiger- Müller Counter. The construction of this detector is shown in Figure 2. Figure 2: The Geiger-Müller Counter In this detector, radioactive particles entering the thin window collide with gas molecules and ionize them. The high voltage across the tube draws the electrons to the positive wire, or anode, and the ions to the outer wall, which acts as a cathode. This current can be detected electronically. The behavior of the counter depends on the applied voltage V. When low voltages are applied to the detector, all of the ionized particles are collected before they recombine. This is called the ionization chamber regime, and is mainly used to detect α-particles. If the voltage is increased, the initial electrons can gain sufficient energy between collisions to ionize further particles, causing an avalanche breakdown. The pulse height across the resistor R is now proportional to both the initial amount of ionization and the voltage V. The avalanche produced is highly localized; when the counter operates in this regime it is called a proportional counter. As the voltage is increased still further, the discharge spreads along the whole wire and gives a very large pulse that is independent of the energy of the initial ionizing event. When the counter operates in this voltage region, it is called a Geiger- Müller counter.
Another important consideration in using particle detectors is the dead time. If two particles arrive at the counter at the same time, only one count will be registered. The time separation necessary for both to be counted is called the dead time τ. Suppose that a source delivers n counts per unit time and that m of these counts are measured. The counter will be insensitive for a time mτ. The number of counts that are missed per unit time is n m = n (m τ). (1) One method of determining the dead time is by the two source method. Suppose that a count rate of m 1 is observed for source A, m 2 for sources A and B, and m 3 for source B. Then n 1 = n 2 = n 3 = m 1 1 m 1 τ m 2 1 m 2 τ m 3 1 m 3 τ Since n 2 = n 1 + n 3, m 2 1 m 2 τ = m 1 1 m 1 τ + m 3. (2) 1 m 3 τ An equation for τ in terms of the three measured count rates can be derived from this equation. Prelab Questions 1. The radioactive source that you will be using is Thallium-204. What is the decay mode of 204 Tl? What particles does it emit? What is their energy? What is its half life? What is the remaining nucleus? 2. Consider a 20,000 Bq source placed 10 cm away from the window of a Geiger tube. The window on the tube is round and 2 cm in diameter. Approximately what count rate do you expect to detect on the Geiger counter? 3. Discuss sources of background count rates that you might expect to encounter. 4. Consider how best to plan your measurement times in order to make sufficiently precise measurement of background-corrected activities. 5. Derive an expression for the dead time τ from Eq. 2. 6. Nuclear engineers refer to material absorber thickness in units of mg/cm 2. Why? What are the conversion factors from this into cm for Al, Pb and air at NTP? 7. From absorption vs thickness curves, it has been deduced that all the β-particles emitted in β-decay of a given nucleus do not have the same energy. Assuming that a fixed amount of energy is released in the β-decay, this implies non-conservation of energy. How is this situation resolved?.
8. As sketched in figure 1, the absorption curve is exponential except for deviations at small and large thicknesses. Show that the intensity of β s is exponential in absorber thickness if the probability of interaction is proportional to the incident intensity and is independent of position z in the slab of material. Apparatus ˆ radioactive source ˆ Geiger-Müller counter ˆ absorbers ˆ platform to support absorbers (top shelf is blocked to prevent accidental damage to the tube.) Experiments Note, as of 2010, the sources in use are sufficiently weak that you should use both together to obtain reasonable count rates for the voltage characteristic curve, aluminum range measurement, and optional experiments described below. 1. Voltage Characteristic of the Geiger-Müller Counter. Before turning anything on, check that the Geiger-Müller tube in the white stand is connected to the scaler-timer and check that the high voltage setting is at the minimum position. Turn on the scaler timer and allow it to warm up for a few minutes. Put the source on the third or fourth shelf from the top. Increase the voltage slowly, note the voltage at which counting starts, and obtain the counting rate at various voltages. DO NOT EXCEED THE MAXIMUM VOLTAGE INDICATED ON THE TUBE MOUNT OR THE TUBE MAY BE DESTROYED. Plot a graph of the counting rate versus voltage and determine the slope of the plateau. Select a voltage near the centre of the plateau and use this in future experiments. This will ensure that the counting rate is approximately independent of voltage. 2. Dead time. Measure the dead time of the Geiger-Müller Counter using the two-source method. 3. The Range of β-particles in Aluminum. Measure the count rate detected by the Counter for various thicknesses of aluminum placed between the Counter and the source. Correct the observed count rates for ambient background counts (that is, background counts in the absence of the source) and plot a graph of the corrected count rate as a function of thickness. Note that obtaining statistically significant count rates above
ambient background at the large absorber thicknesses entails significant counting times. Before taking data, assess the situation at a small and a large thickness and adjust the setup as necessary. Correct your value of the range for (a) the air space between the Geiger tube and the source and (b) the window on the Geiger tube. Using the calibration curve shown in Figure 3, determine the maximum beta energy of your source. 4. Optional: Backscattering. Study the backscattering rate as a function of the thickness of aluminum. Position the source so that β-particles cannot directly enter the window. One way to accomplish this is to mount the detector upside down and to rest the source off to the side of the detector mouth. (Request assistance from the TA for this). At what thickness of aluminum does the backscattering rate saturate? How does this compare with the β-particle range in Al? Energy (MeV) 1 0.1 0.01 0.1 1 10 100 1000 Range (mg/cm 2 ) Figure 3: The range-energy relationship for β-particles in aluminum (L. Katz and A.S. Penfold, Rev. Mod. Phys., 24, 28, 1952). 2009-2 PCH