alpha_particles - The Range of Alpha Particles in Air...

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The Range of Alpha Particles in Air Lennon Ó Náraigh, 01020021 Date of Submission: 5 th April 2004 Abstract: This experiment assumes that the notion of Range is applicable to alpha particles and sets out to calculate said range. In the course of the experiment, the dependence of the range on the geometry of the apparatus will be investigated. In the experiment, it was found that cm R 1 . 0 4 . 3 ± = α for air at room temperature and atmospheric pressure. This compares well with the accepted value cm R 4 . 3 = α 1 . An estimate of the range of alpha particles in water was obtained from the Bragg-Kleeman rule, and was found to be ( 29 [ ] Air Water R R % 01 . 0 16 . 0 ~ ± . 1 H.A. Bethe, U.S. Atomic Energy Commission, Document BNL-T-7, 1949. Energy of alpha-particles: 4.88MeV. These were the conditions of the experiment: Temperature of Air: 15 o C; Pressure: 760mm.
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2 A realization of the foregoing theory is by 4.88 MeV alpha particles (ions with z = 2) travelling through air. These are NR ( s m v / 10 ~ 7 ). Alpha particles are highly ionizing and we expect these to interact strongly with matter. Thus, we expect the intensity of α -radiation to fall off steeply with source-detector distance and this will define the range – the distance at which the intensity becomes zero. This situation is contrasted with electrons, which do not interact so strongly with matter and thus do not exhibit the same strong range-intensity dependence. The rate of a particle’s (ion’s) energy loss, per unit path length, as it passes through a medium, is known as the stopping power , S ¸ of the medium. A quantum-mechanical derivation including relativistic effects was first carried out in 1930 by Bethe and Bloch, and their formula is quoted here: ( 29 ( 29 - - - - = 2 2 2 2 2 2 1 log 2 log 4 β β ρ π I mv Amv N Z ze dx dE S A (1) Where c v β = is the ion velocity and ze is its electronic charge in e.s.u.’s, m the mass of the electron, A, Z, ρ are the atomic mass number, the atomic number and the density of the stopping material, respectively. I is the mean energy required to ionize a particle of the material and is about 86eV for air. As usual, terms in β can be dropped in the non-relativistic (NR) limit. In a naïve treatment of equation 3 (1), we might proceed in the following way: Write ( 29 ( 29 4 2 4 2 2 2 log 1 2 2 log 2 1 2 β ξ ξ β o I C o I mv I mv I C dx dE + - + - = Where the terms in 2 β are self-cancelling. Then, dE C I dE dE dx dx R E E R = = = 0 0 0 2 0 0 log 2 ξ ξ , in the NR limit. Use 2 2 1 v M E α = to change the variable of integration: E IM m M v M I m I mv α α α ξ 4 2 2 1 2 2 2 2 = = = 2 John Lilley, Nuclear Physics, Principles and Applications, (Wiley, 2002) , pp. 130 – 136. 3
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alpha_particles - The Range of Alpha Particles in Air...

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