Energy Loss of Alpha Particles in Matter


Scientific Study, 2019
3 Pages, Grade: 0.82

Excerpt

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

Abbildung in dieser Leseprobe nicht enthalten1

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

Abbildung in dieser Leseprobe nicht enthalten

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:

Abbildung in dieser Leseprobe nicht enthalten

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:

Abbildung in dieser Leseprobe nicht enthalten

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:

Abbildung in dieser Leseprobe nicht enthalten

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.

Abbildung in dieser Leseprobe nicht enthalten

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.

Abbildung in dieser Leseprobe nicht enthalten

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

Abbildung in dieser Leseprobe nicht enthalten

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.

Abbildung in dieser Leseprobe nicht enthalten

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.

[...]


1 L. Porter and S. Bryan, Radiation research 97, 25 (1984).

2 S. Morgan Jr and P. Eby, Nuclear Instruments and Methods 106, 429 (1973).

3 L. Porter and H. Lin, Journal of Applied Physics 67, 6613 (1990).

4 J. Comfort, J. Decker, E. Lynk, M. Scully, and A. Quinton, Physical Review 150, 249 (1966).

5 S. M. Seltzer and M. J. Berger, The International Jour­nal of Applied Radiation and Isotopes 33, 1189 (1982).

6 J. H. Lawrence, C. Tobias, J. Born, J. Linfoot, R. Kling, and A. Gottschalk, Transactions of the American Clinical and Climatological Association 75, 111 (1964).

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Details

Title
Energy Loss of Alpha Particles in Matter
College
University of Manchester  (The University of Manchester)
Grade
0.82
Author
Year
2019
Pages
3
Catalog Number
V509611
ISBN (eBook)
9783346074706
Language
English
Tags
energy, loss, alpha, particles, matter
Quote paper
Juli Okayama (Author), 2019, Energy Loss of Alpha Particles in Matter, Munich, GRIN Verlag, https://www.grin.com/document/509611

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