Alpha particles, or Helium nuclei, are projected by a radioactive isotope source into a vacuum chamber filled by varying thicknesses of either metallic foils (aluminium, nickel) or gases (helium, nitrogen, argon). A Silicon detector, placed at the opposite end of the chamber, detects the final energies of the alpha particles as they penetrate through the media. It is theorised by the Bethe-Bloch equation that the greater the thickness of the medium in the vacuum chamber, the lower the final energies. Through comparison between the Bethe-Bloch equation and experimental data, the ionisation values for the various elements used can be found. Our preliminary results for one such element, aluminium, demonstrate an ionisation value of I=141.2eV.
Energy Loss of Alpha Particles in Matter
Juli Okayama The University of Manchester (Dated: 1st November 2019)
Alpha particles, or Helium nuclei, are projected by a radioactive isotope source into a vacuum chamber filled by varying thicknesses of either metallic foils (aluminium, nickel) or gases (helium, nitrogen, argon). A Silicon detector, placed at the opposite end of the chamber, detects the final energies, Ef , of the alpha particles as they penetrate through the media. It is theorised by the Bethe- Bloch equation that the greater the thickness of the medium in the vacuum chamber, the lower the final energies, Ef . Through comparison between the Bethe-Bloch equation and experimental data, the ionisation values, I , for the various elements used can be found. Our preliminary results for one such element, aluminium, demonstrate an ionisation value of I = (141.2 ± 2.1)eV.
I. INTRODUCTION
This report articulates the variations in alpha particle energy as it passes through varying thicknesses of metallic foils (aluminium and nickel) and gases (helium, nitrogen, and argon). This yields an alpha particle energy distribution, thereby providing a basis for calculating the ionisation energies of the corresponding elements.
When the positively charged alpha particles are projected by the radioactive source and pass through matter, it interacts via the Coulomb force with the electrons bound to the atoms of the medium through which it is travelling. At each collision a small amount of kinetic energy is lost by the alpha particle - if it interacts enough times, it will eventually come to rest. They can also excite or ionise the atomic electrons, providing a physical basis for understanding elemental ionisation energy.
The interactions between projected alpha particles and atomic electrons create positive ions and free electrons. Under the influence of an electric field, these electrons can be collected on an electrode, where the amount of charge is proportional to the number of ionisations and thus the kinetic energy of the alpha particle. This forms the critical basis for nuclear radiation detectors, where the medium is the depletion layer of a semiconductor junction.
The stopping power, defined as the deceleration force acting on charged particles as they interact with matter, is important for additional applications. The stopping power is closely associated with the dose and thus the biological effectiveness of different kinds of radiation. This experiment allows us to understand how this stopping power for alpha particles is affected by the thickness of certain materials; this has provided the scientific foundation for applications of alpha particles in medicine, where it is used to treat cancers through radiotherapy.
II. THEORY
To evaluate the ionisation values for each of the 5 elements utilised throughout the experiment, comparisons to the Bethe-Bloch equation are required. Excluding lower energy ranges, the Bethe-Bloch equation relates the stopping power, — ddx, to the alpha particle energy, E (MeV), and the ionisation energy of the
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where N is the number of stopping atoms per unit volume, and Z is the atomic number of the element. This equation can be simplified for the purpose of this experiment , as alpha particles ejected from the radioactive sources are restricted to the energy range 3 — 8MeV. This is due to the mechanism of production: alpha particles are emitted by large isotope nuclei with high binding energy, and thus do not have enough kinetic energy to overcome this binding energy to have relativistic kinetic energy 2. As a result, the relativistic terms can be ignored. In addition, the correction term, CK , can similarly be ignored, as tightly bound electrons do not interact significantly with the project ed alpha particles 3. Thus, simplified Bethe- Bloch equation is
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The inverse of the stopping power, (ddx ) [1], can be plotted as a function of energy E to calculate the theoretical thickness, or range AR, of the material the alpha particles pass through. This is conducted using the following equation:
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where AR is the range, E 2 is the final alpha particle energy, and E 1 is the initial alpha particle energy. This provides us a basis for the experimental thickness to be compared to the theoretical thickness, AR. The only remaining unknown value is the ionisation value, I. This value can be found by minimising errors, or x[2 ], in comparisons between the experimental and theoretical thickness:
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where a x is the error on the thickness. The corresponding I value for minimised error, x [2] min, is the ionisation value (eV).
Finally, as there were two experimental setups with metallic foils and gases, it is required for a common variable to be defined between the two: this variable is thickness. The thickness of the metallic foils are found by direct measurement. However, this is naturally not possible for gases. Instead, the experimental conditions are compared with conditions at standard temperature and pressure (STP) 4:
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where 1 denotes STP conditions and 2 denotes experimental conditions.
III. METHOD
This experiment utilised two similar sets of apparatus: one for foils, and one for gases. They both consisted of a radioactive source that emits alpha particles, a semiconductor detector, and a vacuum chamber.
In both experimental setups, the first 3 of 4 steps were the same.
The first step was to apply an appropriate bias voltage to the Silicon detector, expanding the depletion region and applying a retardation force to the oncoming alpha particles. The appropriate bias voltage was found by measuring the energy of the detected alpha particles across a range of voltage values - the bias voltage is where the energy saturated.
Thereafter, the apparatus was calibrated by utilising a pulse generator. The detected pulse was aligned with the energy of alpha particles through a vacuum, and as the alpha particle energies for our sources ([244]Cm for foils and [230]Th for gases) are known, the pulse was calibrated to replicate corresponding alpha particle energy. The pulse generator was consequently used to simulate lower alpha particle energies for which experimental data could not be collected, calibrating our apparatus.
Then, before the experiments were conducted, the chamber was evacuated using a vacuum pump.
Finally, either foils or gases were inserted at various known thicknesses, and the corresponding alpha particle energies were measured using the silicon detector.
IV. RESULTS
While experimental results were obtained for all 5 elements, this report will focus on the results for aluminium foil as the processes were the same.
The alpha particle energy distribution was obtained for varying thicknesses of aluminium foil. The variation in alpha particle energy E was consequently plotted as a function of aluminium foil thickness, as shown in figure 1. The plot was then fitted to quadratic and cubic graphs. As predicted by the Bethe-Bloch equation (1), the alpha particle energies decreased as aluminium foil thickness increased.
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FIG. 1. Aluminium: final energy, Ef, of alpha particles as function of thickness, x
The difference between consecutive data points can be used to differentiate energy as a function of x, thereby obtaining the stopping power — The range, AR can now be calculated using equation 2, and the ionisation value, I, using equation 3. Figure 2 shows how minimisation of thickness error gives ionisation energy and the corresponding error.
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The results are shown in the table below.
TABLE 1. Experimental Results
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It is evident that the ionisation energy for elements with a higher number of protons require greater ionisation energy. Indeed, helium gas has the lowest atomic number at Z = 2, and this is reflected as it has the lowest ionisation energy. In contrast, nickel has the highest atomic number at Z — 28, and thus has the highest ionisation energy. Nitrogen (Z — 7), aluminium (Z = 13), and argon (Z — 18) have ionisation energies between these 2 extremes, which follow in order of their respective atomic numbers.
The obtained values can be compared to accepted values of ionisation energy for the corresponding elements 5.
TABLE 2. Accepted Results
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It is initially demonstrable that the obtained ionisation values are of same order as accepted results, indicating consistent results.
Indeed, this is supported by figure 3, which shows how experimental Bethe-Bloch (red) compares with theoretical Bethe-Bloch (dotted blue). It shows that the shape and magnitude of both curves are similar 6.
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However, it is also evident that the errors obtained are comparatively small, a strong suggestion that errors were not comprehensively evaluated.
The primary contributing factors to thickness and ionisation errors are considered to be from holes in the foils, an imperfect vacuum, and measurement errors of final energy. Indeed, many foils had holes and thus not all alpha particles had to pass through media; the vacuum chamber was only pumped to 10-[2] mbar; final energy measurements had significant full-width half-maximums on the order of 1% of peak energy.
Despite this, these 3 contributors are not particularly significant. The greatest contributor to error was most likely from inaccuracies in measurement of foil thickness - the experiment relied on correct labelling of foil thicknesses as no direct measuring equipment was available. While the consistency in foil thickness labelling was tested by measuring alpha particle energies through different foils with same thickness and element, it was impossible to understand whether the labelling showed the correct absolute values.
Similarly, for gases, the thickness and imperfect vacuum are contributors to error. The two greatest contributors to error, however, are the purity of gas and the error in final energy. Throughout usage of the gas apparatus, air leaked into the vacuum chamber. As measurements were taken by propagating from high pressure/thickness to Ombar, error on measurements of low thickness were most likely high, as air was leaking into the chamber throughout the period measurements were being taken.
Indeed, this was reflected in the Bragg curve graphs, as Helium and Nitrogen gas were translated along the y-axis in opposite directions relative to theoretical Bethe-Bloch, a result of oxygen molecules leaking into the chamber. Furthermore, as [230]Th has a significantly lower activity of lOkBq compared to 230kBq for [244]Cm, the count and clarity of the energy peaks were much less defined compared to the foil results. This factor made it difficult to accurately judge where the peak of the energy distribution lay, increasing error on thickness and ionisation energy.
V. CONCLUSION
Ultimately, by comparing experimental data to theoretical predictions of thickness, it can be concluded that experimental data is consistent with the Bethe- Bloch equation. While the data will never be fully consistent with the Bethe-Bloch as it lacks the distinct “bump” at lower energies, the theoretical thickness shows strong correlation with the thicknesses used throughout the experiment. Ultimately, the experiment was accurate in predicting the ionisation values of our various elements, providing a scientific basis for applications of alpha particles.
One key aspect of the experiment that requires improvement is understanding of errors. The errors were implicitly drawn from the minimisation of y[2], but more careful consideration of each individual error would provide more accurate error readings. Indeed, the errors throughout all 5 experiments were generally small in magnitude compared to accepted values of ionisation and corresponding errors. Quantifying considered errors individually would most likely be similar in magnitude to the accepted values.
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- Quote paper
- Juli Okayama (Author), 2019, Energy Loss of Alpha Particles in Matter, Munich, GRIN Verlag, https://www.hausarbeiten.de/document/509611
