The purpose of this experiment was to determine the mass thickness attenuation factor for beta rays when they pass through polyethylene sheets of varying thicknesses. This was done by using an apparatus that measured the seven different intensities and then taking these values, putting them through a number of calculations and finally generating a graph of ln(I_corr) versus the thickness of the polyethylene sheets. Once this graph was created, it was possible to apply a linear fit and using that, it was possible to determine the slope of the line.

The slope was then used to calculate the mass thickness attenuation factor which ended up being (0.197m ± 0.008) g/cm2. This value was then compared to the theoretical value of 0.2 g/cm2 through a percent difference computation. The percent difference was found to be a mere 1 percent which allowed for the conclusion that the results were very accurate. This was further supported by the graph that was generated because it showed the trend that was expected to be seen. Overall, the experiment was quite successful with only one minor, possible source of error and that being a slight misreading of the intensity apparatus which would explain the 1 percent difference.

Objectives:

In this experiment there were a couple different objectives. The first objective was to gain an understanding of mass thickness attenuation through an investigation using beta rays and polyethylene sheets of different thicknesses. The second objective was to gain practice with new and unfamiliar laboratory instruments.

Experimental Procedure:

For this experiment, there were multiple parts to the procedure. The first part was to find the voltage at which the specific G-M counter operates. This was done by first setting the timer to auto and placing the beta tray in the G-M tube. Next, the counter set up was powered on, reset, and started by pushing the button labeled “count.” The voltage was increased in small increments until the unit began to continue to increase on its own. Once this occurred, it meant that the threshold voltage had been determined. After this, 75 volts was added to the threshold voltage and the machine remained at this level for the rest of the experiment.

The next part of the procedure was to determine the background radiation that was present within the environment. This was done by simply turning on the counter, at the previously determined voltage, and taking a ten minute measurement. Once this was completed it was possible to determine what radiation was coming from the samples and what was just coming from the environment. The relative error for the intensity number found during this part of the procedure was then calculated and both values were recorded.

The next part of the procedure was performed to discover the mass thickness attenuation coefficient of beta rays through polyethylene sheets of varying thickness. This was done by placing the beta source in the second level of the counter, placing the polyethylene sheet in the unit also, turning on the counter, and taking a one minute reading. This same procedure was repeated 6 more times, with 6 other polyethylene sheets of varying thicknesses. Each count for all seven polyethylene sheets was recorded, along with the varying thicknesses of the sheets, and both values were used in the final calculations.

Experimental Results:

The plot that was generated from the results can be found on attachment one. The calculations to come to these results can be found on attachment two.

Data Analysis and Discussion:

In this experiment an apparatus was used to observe the way the mass thickness attenuation factor changed when multiple polyethylene sheets of a variety of thicknesses were used. The apparatus that was used, measured the intensity of the radiation in a unit know as counts. Because it is not possible to completely exclude the background noise that is naturally occurring in the environment, it was necessary to take this into account when performing the calculations. For each polyethylene sheet that was used (of which there were seven), the I_corr was calculated. This was done by taking the intensity value given by the apparatus, subtracting the background noise value that was found previously, and then dividing by ten. Once all of these values were calculated, they were then used to find the natural log of I_corr, which ended up being the y value on the graph.

After generating the ln(I_corr) versus thickness graph, a linear fit was applied. It was from the information provided by the linear fit that allowed comparisons to be made between the theoretical and experimental values. The slope of the linear fit was used to calculate the experimental mass attenuation factor and its error which was found to be (0.197m ± 0.01) g/cm2. This value was then compared to the theoretical value of 0.2 g/cm2 through the percent difference equation. The percent difference was found to be 1.35%. The most probably source of error that caused this percent difference is a slight misreading by the apparatus used to measure intensity.

In order to have decreased the possibility of this happening, the unit should have been tested beforehand to ensure that it was working at its full potential. Because the percent difference is so small, however, it can be concluded that not only are the experimental results precise, but that they are also very accurate and can be accepted as the mass attenuation factor. This is also supported by the graph. The value for intensity seen on the graph decreases in an almost linear fashion, as the thickness of the polyethylene sheets increased as was expected. This indicated that as the polyethylene sheets increased in thickness, the intensity of radiation decreased, suggesting that more beta rays were being absorbed.

Conclusion:

Overall, the objectives of the experiment were accomplished. Not only was mass thickness attenuation looked at in great detail throughout the experiment, but it was also investigated further after the fact through comparison of the theoretical and experimental values. According to the results, the beta rays scatter and absorb at a mass thickness attenuation factor of (0.197m +/- 0.01) g/cm2. When this value was compared to the theoretical value of 0.2 g/cm2, it was concluded that indeed it was accurate because it had a percent difference of a mere 1 percent. Furthermore, this percentage could be explained by a simple misreading of the unit used to find the intensity values. Had the unit not made any slight misreading, the percent difference would have been even smaller and the experiment would have been even more successful.

Courtney from Study Moose

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