Manual for deflection of beta particles

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Manual for 5141.05 deflection of beta particles 11.01.11 Ae 5141.05 Figure 1 The apparatus is an accessory for the bench for experiments in radioactivity (5141.

A GM tube with a rather small window is well suited in respect to angular resolution. If a tube with a larger window is used, it should be moved further away from the magnets.

1 Manual for deflection of beta particles Ae Figure 1 The apparatus is an accessory for the bench for experiments in radioactivity ( ) to be placed on the bench instead of the original source holder. To conduct these experiments you also need a beta source and a GM detector with an appropriate counter. A GM tube with a rather small window is well suited in respect to angular resolution. If a tube with a larger window is used, it should be moved further away from the magnets. For demonstration purposes it is convenient to have an acoustic signal from the tube or the counter. Demonstration of the deflection of beta particles Remove the magnet assembly from the apparatus. Adjust the source holder to an angle of 0 (i.e. point the source directly towards the GM tube). Count for 10 seconds or simply listen to the acoustic signal from the counter. Turn the source holder to 90 and count or listen again. The collimated beam of beta particles no longer reaches the GM tube and the count rate is almost zero. Turn the source holder back to 0. After this you should control that the magnets are turned fully clockwise making Figure 2 the magnetic field point vertically down (see fig. 2). Re-mount the magnet assembly on the apparatus. Count or listen again the radiation has disap - peared. Now turn the source holder slowly as shown on fig. 1 while observing the counting rate or the sound. About an angle of 45, counting starts to wake up again and at about 90 the radiation is strongest. There is noticeable radiation all the way up to the maximum deflection at about Two points: 1 Beta radiation is deflected by a magnetic field the radiation consists of charged particles. 2 The radiation does not follow only one circular path the particles are emitted with many different energies. Following the theory of the movement of charged particles in magnetic fields or the 2nd Law of Laplace it may be deduced that beta particles are negatively charged. This requires you to confirm that the field direction is as shown. A small magnet with known polarity may be used for this. Note: Use a plastic covered magnet (like ) for this, to avoid damaging the neodymium magnets of the apparatus. As a check on the observations the magnets may be turned fully counter-clockwise, making the field go straight up. In this case the radiation does not appear again when the source holder is turned. A/S Søren Frederiksen, Ølgod Tel info@frederiksen.eu Viaduktvej 35 DK-6870 Ølgod Fax

Figure 3 The beta spectrum simple version If the strength of the magnetic field and its geome try is known, it is possible to establish a relationship between the deflection angle and the kinetic

The strength of the magnets may vary, here a value of 310 mt is assumed. Check that the magnets are turned fully clockwise; making the field point vertically down (fig.

2 Figure 3 The beta spectrum simple version If the strength of the magnetic field and its geome try is known, it is possible to establish a relationship between the deflection angle and the kinetic energy of the beta particles. This is presented in fig. 4. This graph is also printed in a larges version on a separate sheet of paper. The strength of the magnets may vary, here a value of 310 mt is assumed. Check that the magnets are turned fully clockwise; making the field point vertically down (fig. 2) The magnet assembly should remain in position during the whole experiment. Vary the angle θ between 40 and 140 in 5 steps and find for each angle the count number N in a fixed time interval (e.g. 100 s). Make also a measurement of the background count N 0 for the same time interval with the source completely removed. Use the graph in fig. 4 to find the kinetic energy of the beta particles for each of the angles used. Calculate the corrected counts N - N 0. Draw the energy spectrum i.e. a graph of the cor rected counts versus the energy. The beta source The magnetic field is chosen to fit the spectrum of the beta decay of Y-90. The decay scheme of a strontium / yttrium source is shown below (fig. 5). The decay of Sr-90 cannot be observed with the magnets provided with the apparatus, as the energies are too small. The branching to the excited level in Zr-90 (and the associated gamma decay) are also impossible to observe. In other words, it is only the decay with a maximum energy of kev that is observed in this apparatus. If a 37 kbq (1 µci) source is used, acceptable counts can be reached by counting intervals of 60 or 100 seconds. If the angle is changed in 5 steps, the experiment can be performed in about half an hour. Figure 5 Figure 4

3 The beta spectrum advanced version Overview The previously treated simple version of the beta spectrum illustrates nicely that the beta particles are emitted with a continuous spectrum of energies, although the details of the spectrum are not determined completely correct. The following sections are meant as a help for those wanting a more thorough theoretical treatment of the subject. To determine the right shape of the energy spec - trum, the nonlinear relationship between deflection angle and kinetic energy must be taken into account. This is the topic for the next two sections. In the section The energy of the beta particles the aforementioned relation is presented. In the section Correction for the distribution of the measurement intervals a correction factor is given, which must be used on the count data. After that, in The shape of the beta spectrum, the theoretical expression for the spectrum is presented. In the last section, The Fermi-Kurie plot, an often used method for determining the maximum energy of the radiation is presented. The use of a spreadsheet or similar software is highly recommended. The energy of the beta particles To determine the relation between the deflection angle θ and the kinetic energy E we will assume that the magnetic field is homogeneous with magnetic flux density B between the magnets and zero elsewhere. The radius of the magnets is called R. Let m 0, e and c as usual stand for the rest mass of the electron, the elementary charge and the speed of light. The relation can now be shown to be with fixed angular intervals. (These are determined primarily by the geometry of the collimator as well as the size of the GM tube and its distance from the center of the magnets.) As E(θ) is nonlinear, the counts must be divided by de/dθ, given by where The shape of the beta spectrum The frequency of beta particles emitted with kinetic energies in an interval de around E is given by where F(Z,E) is the Fermi function that describes the influence of the electrostatic attraction of the beta particles by the atomic nucleus. Z is the atomic number of the daughter nucleus. For Z less than about 50, F(Z,E) may be approximated by the expression Where α = 1/137 is the fine structure constant, and the rest of the entities are given by The graph below (fig. 6) shows with a thick, blue line the theoretical spectrum for E max = 2280 kev. The thin red line shows the combined spectrum for E max = 2280 kev and E max = 546 kev, corresponding to a Sr/Y-90 source. The assumptions about the magnetic field are not completely fulfilled, but a decent agreement with the theoretical spectrum (see below) can be obtained by adjusting B or R slightly. As these only appear in the product B R, it doesn t matter which of the two is modified. Correction for the distribution of the measurement intervals If measurements were performed in equally large energy intervals, you would expect proportionality between the observed counts and the theoretical spectrum, given in the next section. In fact, by using this apparatus, measurements are not performed with fixed energy intervals, but rather Figure 6

4 The Fermi-Kurie plot At high energies the Fermi function is almost constant and the energy spectrum can be linearized. If the expression is plotted as a function of E, the result is a straight line that crosses the x-axis in E max. When using this apparatus ( ), the uncertainty of the energy is large for high energies. As seen in the example shown (fig. 7) it may be necessary to discard e few experimental points around E max, that clearly deviates from the straight line (the two lilac points). After doing that, a very fine agreement with the expected Emax is established. Figure 7

5141.05 deflection of beta particles A/S Søren Frederiksen, Ølgod Tel.

5 deflection of beta particles A/S Søren Frederiksen, Ølgod Tel Viaduktvej 35 DK-6870 Ølgod Fax

BETA-RAY SPECTROMETER

14 Sep 07 β-ray.1 BETA-RAY SPECTROMETER In this experiment, a 180, constant-radius magnetic spectrometer consisting of an electromagnet with a Geiger-Muller detector, will be used to detect and analyze