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Radioactivity Build-up In SilverRevised 12/9/2015 02:48:00

Sam Vallentine 430211968The University of Sydney, School of Physics, Senior PhysicsNew South Wales, 2006, Australiae-mail address: sval1475@uni.sydney.edu.au

Abstract: This paper is a report on an experiment conducted to study the radioactive behaviour of silver metal after exposure to neutron bombardment. Different activity lifetimes were identified for the two isotopes of silver and the activity lifetimes were analysed in relation to exposure time, whereby a saturation point was identified for the silver sample.

Keywords: silver irradiation, neutron absorption, radioactive lifetimes, activity saturation time

Radioactivity Build-up In Silver

IntroductionNuclear decay is the process of the nucleus of an atom breaking down into a different kind of atom (by emission of various types of particles) and it occurs because the nucleus is unstable. This occurs naturally but can also be brought about by adding things to a previously stable nucleus. Atoms with identical proton counts but varying neutron counts in their nuclei are called isotopes of that element. The nuclear decay of one atom usually produces nuclear radiation that will readily interact with surrounding atoms, so there are often various chains of decay incidences associated with specific samples, especially those with a mix of different elements.

The main measuring instrument used in this experiment was a Geiger-Mller (GM) counter, which detects - and -particles well, but not gamma or neutrons. This is due to the design and function of a GM counter. A small, metal chamber filled with gas with a thin window that transmits nuclear radiation (but keeps in the gas) contains an anode wire whose complementary cathode is the chamber wall itself. This system, when the radiation ionises the gas, passes a current out to a wire that can be easily measured for analysis. However, there is a short period after detection during which the ionised gas is collected and no further radiation can be detected. This is called dead time and will be discussed in the Procedure section, where it is calibrated for.

The silver samples used in this experiment were irradiated with neutrons from an americium-beryllium source of neutrons. The neutrons from this source have 5.75 MeV of energy, which is in fact too much (i.e. too fast) for interaction with silver nuclei so they must be slowed down to similar, thermal energies (0.3 eV). This is achieved through several inelastic collisions with hydrogen-rich hydrocarbons (paraffin wax, in this case). Hydrogen nuclei are light enough to recoil significantly after a neutron impact, which imparts much of the neutrons kinetic energy onto the hydrogen atom, slowing the scattered neutron down to a speed at which it can enter a silver nucleus.Theory

Silver (Ag) has two naturally occurring, stable isotopes, and , with respective abundances of 52% and 48%[endnoteRef:1] any given sample of the metal. Bombardment with neutrons begins nuclear decay processes for each nuclide, both of which are similar and involve gamma- and beta-emissions. The equations are as follows.

The -decay timescale is in the order of picoseconds - effectively instantaneous when compared to the lifetime of the activated silver - so said lifetime is calculated from the moment neutron exposure ceases. The irradiated Ag-108 nuclide has a half-life, t1/2, of 142.9s and the Ag-110 has that of 24.56s. The half-life of a radioactively decaying substance is the time it takes for half of the original mass to remain un-decayed. Another measuring stick for such decays is the mean lifetime, , which is defined as the time it takes for the un-decayed sample to have reduced by a factor of e = 2.718.... These standard lifetime measurements are related by the equation . This experiment measured these lifetimes and also the relationship between the neutron-irradiation period and the subsequent radioactivity of the sample; i.e. how many beta-emissions per minute could be expected according to neutron exposure time. [1: Abundance of Ag isotopeshttp://periodictable.com/Elements/047/data.htmllast accessed 9/12/2015 02:48:00]

Experimental ProcedureDead Time Calculation for GM Counter

The GM counter used here misses a certain fraction of the total number of -particles that enter its chamber due to dead time. The relationship between actual counts, expected counts, detection time and dead time is as follows.

Where X` is expected counts, X is measured counts, T is detection time and W is dead time. The dead time of the GM counter can be calculated according to the count rates of various combinations of a set of twin carbon-14 samples (which are naturally radioactive). By irradiating, and measuring the rates of both (XB), the left only (XL), the right only (XR), and neither (XN) carbon samples for the same period of measurement (T), the dead time was calculated according the following equations:

Where A, B and C are:

The calibration data are listed in Table 1. The statistical uncertainty of the count values is the square root of the number of counts.

T100 s 0 s

XL20519143.24

XR32476 180.21

XB51069 225.98

XN92 9.59

W0.144ms .042ms

Table 1 - Twin Carbon Data for Dead Time CalculationThe measured dead time, W = 0.144 .042 ms, compares well with the counting software (PRA)[endnoteRef:2] calculation of .191ms. Though this is slightly out of the range of the error, the exact PRA method of dead time calculation is not understood by myself but known to be different to the formula I used, so the two values cant strictly be compared. Additionally, the discrepancy didnt present much of an issue for the purposes of the experiment so it wont be worried about in this report. [2: PRA Software is a counting and analysis software used for nuclear radiation experiments. The programme was written by Marek Dolleiser and is found online at http://www.physics.usyd.edu.au/~marek/pra/]

Activation Lifetime of Silver

In order to reduce the time between irradiation and GM counting a vertical dropping track was used to transport the sample. Figure 1 depicts how the Ag sample was dropped into the Am-Be neutron flux to be held there for a time, and then with the tug of a stick, allowed to fall past and land fixed in front of the GM counter for -particle detection.

Figure 1 - Irradiation and Detection System Schematic

After irradiating a silver sample with the Am-Be neutron source for 16 minutes, the sample was placed in front of the GM counter for 30 minutes. The signal from the GM counter was processed by the computers sound card and then recorded by the PRA program, which noted the time of each beta detection. The data was analysed in QtiPlot to find the double exponential decay fit lines and the mean lifetime of each isotope was calculated. The activity was measured as number of counts over time and was corrected to include possible dead time emissions. The data for this activity is displayed in Figure 2.

Activity Build-up in Silver

The next step was to see how activity builds up according to exposure time. The previous process was repeated but for exposure times of 15, 30, 60, 120, 240, and 480 seconds. The 16min (960s) datum was also included for this section. The expected number of counts as a function of exposure time is expressed thusly:

Where:C = number of countst = exposure time = mean life of active Ag

= neutron flux = efficiency of GM counter = neutron cross-section (for nucleus capture)n = number of target nucleid = transfer time (calculated from fall height and gravity)c = counting time

The Activity build-up graph is found in Figure 3.REsults & discussionThe mean life times for the Ag-107 and Ag-109 isotopes, calculated from the QtiPlot fit analysis, can be read off the data table found within Figure 2. The values are:

These values (with the uncertainties) fit very well with the respective accepted values of 35.43s and 206.19s.

The activity build-up in the silver is documented in Figure 3. The red line is QtiPlots initial guess for the fit and the green line is the same fit but with the known mean lifetimes factored in. revealed that after about seven minutes of exposure to the Am-Be neutron source, the silver had become as radioactive as it could. This asymptotic pattern is expected from a finite source of irradiated nuclei.

Figure 2 - Activity of silver after 16 minutes of thermal neutron bombardment

Figure 3 - Activity buildup in silver over time

acknowledgements1. The University of Sydney School of Physics for the lab notes and equipment.1. Marek Dolleiser for his supervision and help regarding this experiment.

References