NE 3301 Nuclear Engineering Laboratory

Fall 2014

Laboratory Report #5

Range of Alpha Particles

Submitted to

Dr. Rasool Kenarangui, Professor of Nuclear Engineering Laboratory

at

The University of Texas at Arlington

by

Rockford D. Beassie, Jr.

E-mail: rockford.beassie@mavs.uta.edu

in Partial Fulfillment of Course Requirements

Laboratory Experiments Performed: October 24, 2014

Due Date and Time: October 31, 2014, 0900 hrs

Submission Date and Time: October 31, 2014, 0900 hrs

Department of Nuclear Engineering

The University of Texas at Arlington

Arlington, TX 76019

Rockford D. Beassie, Jr. UTA NE 3301 Fall 2014 1

Range of Alpha Particles

Objective:

This investigation is designed to determine the range of alpha particles as they traverse

through air. By determining this range, the amount of excitation energy contained within the

flow field can then be obtained.

Pre-lab Discussion:

An alpha particle is a helium ion composed of two protons and two neutrons [1]. These alpha

particles are emitted when radioactive materials decay to their neutral states. Typical alpha

particles are fast moving, and as such, ionize more than beta and gamma particles. Due to their

size, they lack the momentum of beta and gamma particles, therefore they have sufficiently less

penetration power than these other particles. Typically, alpha particles can be stopped by cloth,

soil, plastics and even skin. Ingestion and/or injection into the human body provide the greatest

hazard to humans. Since these alpha particles travel faster and have less mass than other

radioactive particles, they will have a greater range potential than the others.

Data Analysis:

1. Initial Run

After setting the voltage limit to operate at 940V and the sampling count interval to 60 sec, a

measurement was taken of the applied voltage versus the electron pulse count activity without a

radioactive sampling source. This provided us a measured background count of twenty-two,

which was needed to estimate the dead-time of this system. It was found that our dead-time, noted

as ‘τ’, was equal to 6μs.

Additional measurements were taken at the same settings, incremented from 2cm to 10cm

with an Am-241 test source. Published alpha emission energies for this source were noted to be

5.486 MeV [2]. The results from this experiment were plotted and are shown below in Fig. 1.

Figure 1. Experimental Results for Experimental Test Runs.

y = -397.71x + 1585 R² = 1

0

100

200

300

400

500

600

700

800

900

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5

Inte

nsi

ty

Range (cm)

Rockford D. Beassie, Jr. UTA NE 3301 Fall 2014 2

For this experiment, the lab manual suggested using a sample containing Po-210 [1]. The

published data for that sample was found to be 5.304 MeV [4]. However, due to its short half-life,

this material had to be replaced with Am-241 because the original Po-210 sample had already

expired to its ground state.

2. Dead Time Calculations

After collecting that data for this experiment, the pulse intensity (noted as “counts”), had to be

corrected to produce the graphs shown in this report. This was done by applying a correction

factor sampled counts. The equation used to calibrate these results is shown below in Equation

(1), along with tabulated results for each test run in Table 1. Note that as mentioned previously, τ

= 6μs.

𝑆 = 𝑛

1+𝑛𝜏 (1)

Table 1. Tabulated Correction Factors.

3. Energy Validations

After determining the true count rates, this data was then compared to the results plotted in

Fig. 1, by looking at the initial decay rate (as drawn) to determine the energy potential within the

flow field. These results were extrapolated to an “effective” ground state and found to occur at

approximately 4 cm. By using the energy versus range equation, as derived below in Equations

(2-3) from Sorrensen and Phelps formula for Alpha range in air [2]. This provided the effective

energy potential within the flow field. These results are also shown in Table 1, and Fig (2-3).

Figure 2. Energy Potential for this Experiment.

1 0 22 60 0.9999994 0 0 0

2 940 812 60 -19.999712 -19.999712 2 -0.025328759 3.358131948

3 940 414 60 -18.999715 -18.999715 3 -0.024062307 4.400397702

4 940 273 60 -17.9997192 -17.9997192 4 -0.022795856 5.330702187

5 940 198 60 -16.9997246 -16.9997246 5 -0.021529407 6.185731936

6 940 168 60 -15.9997312 -15.9997312 6 -0.020262959 6.98519594

7 940 116 60 -14.999739 -14.999739 7 -0.018996513 7.741226703

8 940 109 60 -13.999748 -13.999748 8 -0.017730068 8.461962259

9 940 98 60 -12.9997582 -12.9997582 9 -0.016463625 9.153196074

10 940 63 60 -11.9997696 -11.9997696 10 -0.015197183 9.819237383

Run Voltage Counts Elapsed Time Corrected Counts Average Counts Distance (cm) I/I0 Energy (Mev)

0

1

2

3

4

5

6

7

8

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5

En

erg

y (

Me

V)

Range (cm)

Rockford D. Beassie, Jr. UTA NE 3301 Fall 2014 3

Figure 3. Energy versus Range Results for Americium–241 Alpha Particles.

𝐸 = 0.325𝑅3/2 (2)

𝑅 = (𝐸

0.325)

2/3

(3)

Conclusions:

Based on the results shown in Figure 3, the effective alpha energy for this

experiment was found to be 5.35 MeV. The published alpha energy emission for the Am-241 sample was found to be 5.486 MeV [3]. Thus, a calculated error margin of 2.48% was obtained from Equation (3). The results of this report are also shown below in Table 2.

% 𝐸𝑟𝑟𝑜𝑟 = (|𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑−𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙|

𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙) × 100 (3)

Table 2. Experimental Versus Theoretical Comparisons.

Suggested Lab Manual Sample: Po-210

Po-210 Published Alpha Energy (MeV): 5.304

Actual Experimental Sample: Am-241

Am-241 Published Energy (MeV): 5.486

Experimental Energy (MeV): 5.35

% Error: 2.47903755

Range Equation: R = (E/.325)^(2/3)

Sorrensen and Phelps formula for Alpha range in air[2]: E = 0.325R3/2

44.14.24.34.44.54.64.74.84.9

55.15.25.35.45.55.65.75.85.9

6

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5

En

erg

y (

Me

V)

Range (cm)

Rockford D. Beassie, Jr. UTA NE 3301 Fall 2014 4

The lab manual for this experiment suggested finding an average count value at different measured

distances and derive the intensity from each measurement. The energy could then be determined by taking

the mean value from these measurements. This method was also performed, and is shown in the Appendix,

under Fig. 4, but I feel the method used in this report provided better results.

References:

[1] Kenarangui, Rasool, “Range of Alpha Particles”, Introduction to Nuclear

Engineering Laboratory Manual, 2014, pp. 1-4.

[2] Williams, Trip. "Alpha and Beta Ranges." Alpha and Beta Ranges. Alpharubicom, 31 Mar. 2009. Web. 30 Oct. 2014. <http://www.alpharubicon.com/basicnbc/article16radiological71.htm>. Copyright 1996-2009. [3] "Polonium-210: Factfile*." Nucleonica: Polonium-210. European Atomic Energy Community, n.d.

Web. 31 Oct. 2014. <http://www.nucleonica.net/polonium210.aspx>. Copyright 2007-2014.

[4] Firestone, R.B., and L.P. Ekström. "Table of Isotopes Decay Data." Table of Isotopes Decay Data.

N.p., n.d. Web. 31 Oct. 2014. <http://ie.lbl.gov/toi/nuclide.asp?iZA=950241>.

Appendix:

Figure 4. Experimental Data Analysis.

Description Suggested Lab Manual Sample: Po-210 Po-210 Published Alpha Energy (MeV): 5.304 Actual Experimental Sample: Am-241 Range Equation: R = (E/.325)^(2/3)

Number of Runs 0 Dead Time= 6 us Am-241 Published Energy (MeV): 5.486 Sorrensen and Phelps formula for Alpha range in air: E = 0.325R3/2

Preset Time 60 Experimental Energy (MeV): 5.35 http://www.alpharubicon.com/basicnbc/article16radiological71.htm

Pause Time 0 22 % Error: 2.479038

Alarm Level 0

High Voltage 940

Step Voltage 0

Volume 0

Corrected AverageRun High Elapsed Counts Counts Distance (cm) Distance (cm) Energy(MeV)

Number Voltage Counts Time Date/Time I/I0 Energy (Mev)

1 0 22 60 10/24/2014 21.9997096 0 0 0 0 0

2 940 812 60 10/24/2014 789.6048766 789.6048766 2 1 3.358131948 0.1 0.455768626

3 940 414 60 10/24/2014 391.8974783 391.8974783 3 0.496321 4.400397702 0.2 0.723487596

4 940 273 60 10/24/2014 250.9555803 250.9555803 4 0.317824 5.330702187 0.3 0.948036946

5 940 198 60 10/24/2014 175.9767708 175.9767708 5 0.222867 6.185731936 0.4 1.148464971

6 940 168 60 10/24/2014 145.9833577 145.9833577 6 0.184882 6.98519594 0.5 1.332675547

7 940 116 60 10/24/2014 93.99221736 93.99221736 7 0.119037 7.741226703 0.6 1.504914845

8 940 109 60 10/24/2014 86.99316226 86.99316226 8 0.110173 8.461962259 0.7 1.667796735

9 940 98 60 10/24/2014 75.99452833 75.99452833 9 0.096244 9.153196074 0.8 1.823074504

10 940 63 60 10/24/2014 40.99790909 40.99790909 10 0.051922 9.819237383 0.9 1.971996315

1 2.115490565

1.1 2.254271478

1.2 2.388903408

1.3 2.5198421

1.4 2.647462292

1.5 2.772076846

1.6 2.893950385

1.7 3.013309265

1.8 3.130349024

1.9 3.245240047

2 3.358131948

2.1 3.469157009

2.2 3.578432915

2.3 3.68606495

2.4 3.792147783

2.5 3.896766938

2.6 4

2.7 4.101917633

2.8 4.202584427

2.9 4.302059619

3 4.400397702

3.1 4.497648953

3.2 4.593859885

3.3 4.689073633

3.4 4.783330297

3.5 4.876667238

3.6 4.969119334

3.7 5.060719217

3.8 5.151497465

3.9 5.241482788

4 5.330702187

4.1 5.41918109

4.2 5.506943486

4.3 5.594012035

4.4 5.680408174

4.5 5.766152204

4.6 5.851263379

4.7 5.935759979

4.8 6.01965938

4.9 6.102978116

5 6.185731936

5.1 6.267935856

Suggested Lab Manual Sample: Po-210 5.2 6.349604208

Po-210 Published Alpha Energy (MeV): 5.304 5.3 6.4307506815.4 6.511388366

5.5 6.591529787

Actual Experimental Sample: Am-241 5.6 6.671186941

Am-241 Published Energy (MeV): 5.486 5.7 6.750371324

Experimental Energy (MeV): 5.35 5.8 6.829093964

% Error: 2.47903755 5.9 6.9073654476 6.98519594

Range Equation: R = (E/.325)^(2/3) 6.1 7.062595218

Sorrensen and Phelps formula for Alpha range in air: E = 0.325R3/2 6.2 7.13957268

http://www.alpharubicon.com/basicnbc/article16radiological71.htm 6.3 7.216137374

6.4 7.292298015

6.5 7.368062997

6.6 7.443440418

1 0 22 60 0.9999994 0 0 0 6.7 7.518438088

2 940 812 60 -19.999712 -19.999712 2 -0.025328759 3.358131948 6.8 7.593063546

3 940 414 60 -18.999715 -18.999715 3 -0.024062307 4.400397702 6.9 7.667324072

4 940 273 60 -17.9997192 -17.9997192 4 -0.022795856 5.330702187 7 7.741226703

5 940 198 60 -16.9997246 -16.9997246 5 -0.021529407 6.185731936

6 940 168 60 -15.9997312 -15.9997312 6 -0.020262959 6.98519594

7 940 116 60 -14.999739 -14.999739 7 -0.018996513 7.741226703

8 940 109 60 -13.999748 -13.999748 8 -0.017730068 8.461962259

9 940 98 60 -12.9997582 -12.9997582 9 -0.016463625 9.153196074

10 940 63 60 -11.9997696 -11.9997696 10 -0.015197183 9.819237383

Run Voltage Counts Elapsed Time

Counts W/O Source =

From Range Equation:

Corrected Counts Average Counts Distance (cm) I/I0 Energy (Mev)

y = -397.71x + 1585R² = 1

0

100

200

300

400

500

600

700

800

900

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5

Inte

nsi

ty

Range (cm)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5

I/I0

Mean Range (cm)

0

1

2

3

4

5

6

7

8

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5

En

erg

y (

Me

V)

Range (cm)

4

4.1

4.2

4.3

4.4

4.5

4.6

4.7

4.8

4.9

5

5.1

5.2

5.3

5.4

5.5

5.6

5.7

5.8

5.9

6

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5

En

erg

y (

Me

V)

Range (cm)