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To find the range of Alpha Particles in Air
Oisin De Conduin
Abstract
This experiment was conducted in order to find the range of alpha particles in air. The range in water was also estimated. For 4. 88 M eV alpha particles, the range was found to be 36 ± 2 mm, which corresponds to the given value of 35mm within scientific error. The range in water was estimated as 38 microns.
Introduction
Alpha Particles and Bragg Curves
When alpha particles are emitted from a radioactive source, they travel a well defined distance based on the stopping power of the material they are travelling through and their initial energy. The aim of this experiment was to find the range of the alpha particles in air. A 209 Po source was used, which emits alpha particles with energies of 4. 88 M eV. The reason for this well defined range is that when a charged particle moves through some material, it ionizes the atoms of the matter around and loses energy. The stopping power of a material is defined as the average loss of energy per unit length of path travelled for a given particle. If you plot the stopping power vs path length you will get a Bragg Curve, an increasing curve reaching a peak before dropping rapidly to zero. The peak is called a Bragg Peak.
Figure 1: Bragg Curve
The stopping power is defined as : S(E) = −dxdE
Solid Angles
In this experiement, it is also necessary to used solid angles to analyse the data. The unit of solid angle is defined as the solid angle subtended at the centre of a sphere of unit radius by a region of the sphere whose area is one square unit. This is a steradian. For a spherical cap of area A and spherical radius R, the solid angle Ω is given by: Ω = (^) RA 2 The area, A, of the spherical cap is simply 2πrh where h is the height of the cap. For a disk facing another disk, the solid angle is given by:
R
d
S
d
∫ S
0 Ω( ∫d, R, x )xdx S 0 xdx
In the special case when R = S, the values for Ω as a function of Rd are given by the table below:
R/d Solid Angle (Str.) R/d Solid Angle (Str.) 0.1 0.031 0.9 1. 0.3 0.250 1.2 1. 0.6 0.770 1.8 2. 0.8 1.124 2.4 2.
Using this data, a graph was plotted to find other values of Ω for Rd :
Figure 2: Rd vs Solid Angle
Results and Conclusion
Range in Air
The Count Rate over 10 minutes for varying height H was recorded. Results are shown as follows:
Height(mm) Count Height(mm) Count 0 1729 20 154 2 1119 25 57 4 848 26 31 6 693 27 20 8 563 27.5 19 10 473 28 12 12 349 28.5 8 14 271 29 6 15 262 30 6 16 223 40 6 18 194 50 6
Using this data, a graph of the count rate against the distance d between the source and the detector was plotted:
Figure 4: Count Rate against Distance
The graph is similar to that of the Rutherford scattering, with the count rate decreasing exponentially as the distance increases. If alpha particles have a well defined range, we would expect to see an almost constant line with a
steep drop to zero at the limit of the range. This is not the case however, as the probability of detection by the counter is proportional to the area of the counter and the source detector distance. Hence we analyse our data using the solid angle between the source and the detector. Initially, the solid angle Ω was estimated, assuming the source is a point and the detector is a spherical cap rather than a flat disk. Then a graph of C Ω vsd was plotted as shown:
Figure 5: C Ω vs d for estimated Ω
The graph goes to zero in the region of 36 ± 2 mm Subsequently, the actual solid angle was calculated,
Errors
The errors on the x-axis of the graphs are quite small. This is due to the fact that the distance between the source and the detector at its lowest point is known (9.0mm) and that the variation in the height was measured with a vernier calipers. There was no calculations involved with this data. For the estimated solid angle, the error in the count (
C) is the cause for most of the uncertainty. This could be reduced by taking additional counts at each distance, or by taking counts over a longer period of time. The largest errors are in the graph of the actual solid angle. This is due to the fact that there wasn’t enough information given about the relationship between Rd and Ω. While nine points were given, esentially only three of these were in the range that we were investigating.
