Testing of Radiation Shielding and Calculation of Half-Lives

ByWilson Punyalack, Abdolmajid Raeisi, Yi-Hsuan Chiu, Supun Bakiwewa, Chiyoko Yagasaki and Lewis Risk

AbstractRadioactivity, scientifically speaking is a relatively new pursuit of science and in this day and age has proven to be one of the most beneficial discoveries. In this report the types radiation that were studied were alpha, beta and gamma which all have different properties which were tested through shielding and half life calculations. It was found that lead was the best form of shielding but only after taking into account the amount of flaws present in the experimental design.

Introduction : In the past one hundred years, the study of radioactivity has been explored and established. This field of study was introduced in the late 19th century, and later firmly established by French scientists Marie Curie and Pierre Curie with their experiments on radioactive elements (Hocking, 2005). Radioactivity is at the cutting-edge of modern science for its significance in medical application as well as archaeological and environmental importance.

The report describes the experiment designed and conducted in order to record the absorption of different types of radiation by various materials; additionally, the decay of radioactivity was also measured. The results of absorption were compared between different materials and the half-life of various radioactive sources was calculated form the data obtained.

Theory:

When an unstable nucleus decays it may give off several forms of radiation, three well known forms of radiation that were measured in the first experiment were Alpha, Beta and Gamma radiation. Each of these forms of radiation, or ionising radiation, has different properties which affects how they interact with matter. Alpha radiation consists of two protons and two neutrons and being a relatively large particle lacks the penetrating power of other forms of radiation as it is quickly ionises. Beta radiation is a single electron and due to its small size and high speed can penetrate more thicker shields. Gamma radiation is a ray rather than a particle and is usually given off with alpha and beta radiation. It is less ionising than the other forms of radiation as it does not have a charge and as such is extremely penetrating. The second experiment involved calculating the half life radioactive isotopes. This involves measuring the amount of radiation over a period of time and the half life is calculated when the radiation emitted is half that of the initial measurement. The general formula for half life is:

Where Nt Is the final amount, N0 is the initial amount, t is the time passed and t1/2 is the half life.

Materials and methods:

Materials:

Part I: radiation shielding

Geiger-MÜller counter w/ GM TUBE (detector) Stop watch Latex gloves Radioactive sources:

Alpha 37 kBq Am-241 (1987) Beta 37 kBq Sr/Y-90 1μCi (1985) Gamma 370 kBq Cs-137 10μCi (1985)

Sheets of Paper Thin aluminium blocks Thick aluminium blocks Lead Blocks Plant material (leaf, bark) Meat material (beef patty) Wood blocks

Part II: Radiation half-life

Geiger-MÜller counter w/ GM Tube (detector) Stop watch Microsoft excel Radioactive sources:

Alpha 37 kBq Am-241 (1987) Beta 37 kBq Sr/Y-90 1μCi (1985) Gamma 370 kBq Cs-137 10μCi (1985) Barium -137m minigenerator

Methods:

Both parts of the experiment were performed under standard laboratory conditions at room temperature.

Part I: Radiation Shielding

Apparatus consisting of a Geiger counter and GM tube (gaseous ionisation detector) were appropriately organised and set up. The GM tube was situated 15cm from radioactive source propped by a support bracket ensuring stability. Background radiation checks were performed 5 times; the average utilised as appoint of reference. Background radiation was accounted for simply by switching on the Geiger counter and observing the produced numerical value after 1 min. Standardised sources of alpha, beta and gamma radiation were then positioned in the support bracket (handling requires use of latex gloves). The radioactivity of each source was recorded

over a period of 1min through four trials. These standards are used as a source of comparison.

Following standard measurements, the different shielding materials selected were individually placed in between the radioactive source and the GM tube. Each of the shielding materials was subjected to all three types 1 min of radiation over a number of 4 trials each. The amount of radiation able to penetrate the shielding material was determined by the Geiger counter. These results were then entered into Microsoft Excel of detailed analysis.

This proved to be scientifically unreliable as there were two variables being changed. As such modifications were made to the experiment whereby there would be only one variable being changed. That is, rather than using different shields of different thicknesses the experiment was carried out using shields of the same thickness and after each measurement the shields were made thicker until a the value for radiation remained relatively consistent.

Part II: Calculating Half Life

Similarly, apparatus consisting of a Geiger counter and GM tube (gaseous ionisation detector) were appropriately organised and set up. Background radiation checks were performed 3 times over a time period of 5 min each.

To determine the half life of each radioactive substance (alpha, beta and gamma), each sample was securely positioned into the support bracket over 5 min. Radiation levels were noted in 30sec intervals. The radiation emitted over each 30 second interval can be calculated simply by means of subtraction.

The results were processed in Excel and the appropriate graphs were produced for analysis.

Results:

Shielding Experiment:

The following results depict graphs of radiation penetration through various thicknesses of shielding.

Thickness vs Radiation (Alpha-Wood)

y = 30.872e-0.0304x

R2 = 0.917

0

10

20

30

40

0 10 20 30 40 50

Thickness (mm)

Rad

iati

on

Thickness vs. Radiation (Aplha-Lead)

y = 29.093e-0.0789x

R2 = 0.9366

0

10

20

30

0 5 10 15 20 25 30

Thickness (mm)

Rad

iati

on

Thickness vs. Radiation (Alpha-Aluminium)

y = 37.044e-0.05x

R2 = 0.8716

0

10

20

30

40

0 5 10 15 20

Thickness (mm)

Rad

iati

on

Figure 1 – Alpha Radiation and Shielding

Thickness vs.Radiaton (Beta-Wood)

y = 123.21e-0.0698x

R2 = 0.8488

0

50

100

150

200

0 10 20 30 40 50

Thickness (mm)

Rad

iati

on

Thickness vs. Radiation (Beta-Lead)

y = 34.071e-0.0745x

R2 = 0.8937

05

101520253035

0 5 10 15 20 25

Thickness (mm)

Rad

iati

on

Radiation vs. Thickness (Beta Aluminium)

y = 113.97e-0.0873x

R2 = 0.968

0

20

40

60

80

100

120

0 5 10 15 20

Thickness mm

Rad

iati

on

Figure 2 – Beta Radiation and Shielding

Radiation vs. Thickness (Gamma Wood)

y = 121.78e-0.0039x

R2 = 0.7083

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30 35 40 45

Thickness (mm)

Rad

iati

on

Radiation vs. Thickness (Gamma Lead)

y = 124.61e-0.0722x

R2 = 0.9573

0

20

40

60

80

100

120

140

0 5 10 15 20 25

Thickness mm

Rad

iati

on

Radiation vs. Thickness (Gamma Aluminium)

y = 120.35e-0.0123x

R2 = 0.9943

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16

Thickness mm

Rad

iati

on

Figure 3 – Gamma Radiation and Shielding

From these graphs it is clear that the thicker the shield is the more radiation it will stop, however – depending on the nature of the radiation certain materials will only affect the radiation measured slightly. Lead was the best shield due to it’s high density followed by aluminium and then paper. From these results the Amount of radiation measured is inversely proportional to the Thickness and Density of the shielding material.

Half – Life Experiment:

Initially the half-life experiment was conducted on the first three radiation emitters used in the shielding experiment. The follow depicts results of the measurement of the three radioactive isotopes over 5 minutes at 30 second intervals.

Figure 4 – Alpha Radiation Half Life results

Figure 5 – Beta Radiation Half Life results

Figure 6– Gamma Radiation Half Life results

However due to problems encountered instead Cs-137 was reacted with an acid forming Ba – 137m to give the following results over five minutes:

Time (mins)

β -radiation (Cs-137 Liquid)

ratio of β -radiation reduction

0.5 401 11 358 0.89276808

1.5 353 0.8802992522 302 0.753117207

2.5 207 0.5162094763 298 0.743142145

3.5 216 0.5386533674 162 0.403990025

4.5 152 0.3790523695 144 0.359102244

Table 1: The change of the β -radiation for Cs-137 liquid against time

The change of the β-radiation for Ba-137m liquid against time is shown in Table 1. Since our purpose of this experiment is to find out half-life, the ratio of β -radiation reduction was calculated and indicated next to the β -radiation column. The β -radiation for Ba-137m liquid decreased at a certain ratio.

Figure 7 shows the ratio of β -radiation reduction versus time. According to exponential trend line, we obtained: y=1.1713e-0.2394x

where x is time in minutes and y is the ratio of β -radiation reduction, and R2 = 0.8905.

Figure 7; the ratio of β -radiation reduction versus time

I2 radiation reduction ratio

y = 1.1713e-0.2394x

R2 = 0.89050

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6

Time (mins)

ratio

of

I2-r

adia

tion

redu

ctio

n

ratio of I2- radiationreduction

Expon. (ratio of I2-radiation reduction)

β

Figure 8; β -radiation against time

The β -radiation against time was illustrated in Figure 8. From this graph, we obtainedY = 469.7e-0.2394x where R2 = 0.8905.

From the equation from the graph R2D, when y=0.5 X = 3.56187 mins From the equation from the Figure 8, half life is where y= 0.5*469.7And we have the same answer as before, namely X = 3.56187 mins

I2-radiation

y = 469.7e-0.2394x

R2 = 0.89050

50100150200250300350400450

0 2 4 6

Time (mins)

I2-radiation

I2-radiation (Cs-137Liquid)Expon. (I2-radiation(Cs-137 Liquid))

β

Discussion:

In this experiment there were several results that were considered unreasonable or more so that they did not fit into what was already known about physics. They were:

That a sheet of paper blocked more radiation than a sheet of aluminium in the alpha particle tests

That a meat patty overall blocked more radiation than a sheet of lead (one of the most dense elements)

Other than these results most of the other results were consistent with experiments that were carried out previously in history.

However the results achieved in this experiment can not be considered reliable as they differ from what is has begun to be expected from the global scientific community.This is due to many factors, mainly:

The Background Radiation was constantly fluctuating. Other radioactive sources were within relatively close proximity to the Geiger

counter and as such individual measurements could not be considered accurate.

The experiment itself was badly set out, involving insufficient variable control as well as inappropriate radiation sources.

Background Radiation – Due to the nature of radiation it is very difficult to achieve the same results twice in a row; this is because the way a particle can be emitted is essentially random. Taking this into account the Background radiation during our testing was seen to fluctuate considerably between 17 to 26 Geiger clicks meaning that our final calculations of the radiation emitted by a radioactive source was inaccurate. While this was partially solved by repeating the measurements several times it was never completely possible to remove all chance of error considering how radiation is never consistent.

Uncontrolled Radioactive Sources - During initial measurements, the serious mistake was made of leaving other radioactive sources near the Geiger counter, this created extremely varying results and by consequence had to be redone. This was solved by placing the radioactive sources in a shielded box which was found to sufficiently reduce the inaccuracies in results obtained; however the effectiveness of this is still unknown creating greater doubts of accuracy in the experiments.

Experimental Design Flaws – In both parts of the experiment there were serious flaws. In the first experiment there was insufficient variable control, meaning that while we used different types of shielding as one variable the thickness of these shields were inconsistent. This caused practically all our results to be inaccurate as was demonstrated by how a sheet of paper blocked more than a sheet of aluminium. This was due to the paper being around five times thicker than the aluminium. This also explains how meat was found to be a better method of radioactive shielding than lead. Because of this a new experimental design was created for the first experiment. The second part of the experiment was also poorly designed as the measurement of

the half-life could not be obtained from the samples we were given. As shown by the graphs R2A, R2B and R2C the trend line was not exponential at all and results obtained were far too erratic to be considered for calculations. This was due to the fact that Americium – 241 has a half life of approximately 400 years, Strontium – 90 a half life of 30 years and Caesium – 137 a half life of 28 years (Plambeck, 1996). Ideally to measure the half life of a radioactive substance it must either be done over several years, or have a short enough half life to be measured in a laboratory session (Knight, Jones and Field, 2007). The attempted solution to this was to use Caesium – 137 reacted with acid to modify its half life and radioactivity. The downside to this is that it becomes irrelevant to the experiment at hand as it is a modified radiation emitter meaning it can not be compared to the other emitters which were standard.

Improvements to the Experimental Design –

Shielding Experiment:

Set a certain value of Geiger clicks and incrementally increase the thickness of the shield used until after a certain time the radiation level is reached. The more difficult of the two options as it involves the most precision when using both the Geiger counter the improvement in results above the first option is debatable but will provide intuitive results. I.e. the shield which required the shortest length to reach the amount of clicks with the specified time would be the best shield.

Half-Life Experiment:

If possible find other sources of Alpha Beta and Gamma radiation each with a half life within five to ten minutes.

Conclusion: In the tests conducted it was found that a shield of high density as well as thickness would prove to be the best form of shielding from radioactive sources. Unfortunately this could not be elaborated on through investigation into the half lives of alpha, beta and gamma sources due to the unreliable design of the experiment.

References:

1. Toby Dylan Hocking, (2005), The History of Modern Physics, Berkley University

2. Knight, Jones and Field, (2007), College Physics, Pearson International3. James A. Plambeck, (1996), Chemical Sciences Data Table

Acknowledgements:

Wilson Punyalack – Speech, ReportAbdolmajid Raesisi – Measurements, CalculationsYi-Hsuan Chiu – Research, Report, Supun Bakmiwewa – PowerPoint, CalculationsChiyoko Yagasaki – PowerPoint, Record KeepingLewis Risk – Speech, Measurements, Report