Physics Laboratory Report on Alpha

and Beta Radiation

J. Shapiro and K. ShpundHebrew University of Jerusalem

Racah Institute for Physics

Original: December 14th, 2006Revised: January 25th, 2007

Abstract

What follows is a survey of the basics of alpha and beta radiationtheory, succeeded by a description of an experiment performed as part ofthe third year undergraduate physics laboratory course.

The experiment itself consisted of calibrating the detection system,measuring the half-time of Thorium-228 daughter isotopes radiating withalpha, measuring the slow-down in distance within a medium (Nitrogen)using the Bethe formula, and finally, measuring the decay in time of betaradiation.

1 Introduction

In daily life, we (consciously) encounter ”radiation” mostly when dealing withcell phones. Not much is known other than that there are two types of radiation:ionizing and non-ionizing, and that ionizing is rather more hazardous than non-ionizing. But what is radiation, to begin with?

In order to answer this question, one must first realize what matter is madeof. During the beginning of the twentieth-century, physicists and chemists wereoccupied with this very question. In the end, one model came to prominence,which says basically that matter is made of tiny particles called atoms. Eachatom is comprised of sub-parts in itself: a nucleus containing protons and neu-trons and electrons, ”orbiting” the nucleus. The protons and neutrons withinthe nucleus are rather heavy in mass compared to the electron (mp ≈ 1758×me).The protons have a positive electric charge, the electrons have a negative charge,and the neutrons are neutral. Atoms differ from one another by the number ofnuclei particles they contain.

An isotope is each of two or more forms of the same element that containequal numbers of protons but different numbers of neutrons in their nuclei, andhence differ in relative atomic mass but not in chemical properties. Radiation

1

is, in essence, the process in which an atom decomposes, or rather, decays, intoanother atom (that is, with a different number of nucleons or electrons) anda resulting particle. The resulting particle can be an alpha particle, a betaparticle, or a gamma one1. This resulting particle is radiated in the process ofdecay. The radiation is called ionizing if the resulting particle ionizes the atomsof the matter which comes in its way - if it has enough energy to pull electronsout of orbitals, and non-ionizing if it does not.

The process in which atoms decay into other atoms has been found (empir-ically) to follow a certain pattern. If at time t = 0 we have a quantity N0 ofatoms of a certain matter, then the number of atoms of this matter at furthertimes, t > 0, is given by:

N(t) = N0exp(−λt)

λ is the disintegration constant. It signifies the chance that an atom will decay,per unit of time. The assumption that this value is constant, in time, is funda-mental to the statistical science of radioactivity. The half-life time is defined asthe amount of time in which exactly half of the matter decays. It is given by:

t1/2 = −ln( 1

2 )λ

=ln(2)

λ

The average life-time is defined as the average time before an atom decays.τ = 1/λ.

1.1 Alpha Radiation

Alpha radiation is the result of an abundance of energy of the nuclei, and ofdifference binding energies between different nuclei. A Coulomb repulsion effectalso takes place during the radiation. This repulsion is of a greater importanceto heavy nuclei since the disruptive Coulomb force increases with size at a fasterrate, ∼ Z2 (where Z is the number of protons in the interaction), than does thespecific nuclear binding force, which increases as A (A is the atomic mass). Thealpha particle is ’chosen’ to be emitted from the nucleus since it is a very stableand tightly bound structure - it has a relatively small mass compared to themass of its separate constitutes. In the process of decaying from one state toanother, the nucleus emits an alpha particle and loses a relatively light element(the alpha particle) and thus gets to release the largest amount of energy andconvert it to kinetic energy. The spontaneous emmision of an alpha particle canbe represented by the following process:

AZXN −→A−4

Z−2 X ′N−2 + α

where A refers to the atomic mass, Z refers for the number of electrons, and Nrefers to the number of neutrons. The alpha particle of this process is a nucleusof a Helium atom, consisting of two protons and two neutrons. To understandthis process we must bear in mind the conservation of energy, linear momentum,

1See the next sections for a brief overview on some of those particles.

2

and angular momentum. We assume that the decaying nucleus is at rest, thusit has only a rest energy - mXc2. The final state consists of X’ and the alphaparticle that move in opposite directions (to conserve linear momentum). Thusthe the final total energy is mX′c2 + TX′ + mαc2 + Tα, where T represent thekinetic energy of the particle. Conservation of energy gives:

mXc2 = mX′c2 + TX′ + mαc2 + Tα ⇔ (mX −mX′ −mα)c2 = TX′ + Tα

The quantity on the left side (denoted by Q = (mX −mX′ −mα)c2) of the lastequation is the net energy released in the decay. It is apparent that the decaywill occur spontaneously only if Q > 0. Because the original nucleus is at rest,the the linear momentum at start is zero. Thus, pα = pX′ . The typical releaseof energy is about 5Mev, thus the kinetic energy of both X ′ and the alphaparticle is significantly smaller than mc2, and it is safe to use non-reletavisitckinematics. Writing T = p2/2m, the kinetic energy of the alpha particle isobtained in terms of Q:

Tα =Q

1 + mα

mX′

1.1.1 Alpha Tunneling

According to classical physics, a particle of energy E (the alpha particle), whichis less than the potential energy of the system - in our dicussion the alphaparticle has less energy than the potenial energy that keeps the nucleus fromdisintergrating - is said to be in a potential well. This terminology refers to thefact that the emitted alpha particle (which is positively charged) was under theconstraint of the same potential well, with the approximation that the alphaparticle is a free particle. Solving Schrodinger’s equation for the alpha particle,results with a wave-function that has finite (instead of zero) probability to findthe particle outside the nucleus. Classically, however, there is no reason to findthe alpha particle outside the nucleus since it has lower energy than that of thepotential well which the nucleus creates.

1.2 Beta Radiation

The most basic beta radiation process is the conversion of a proton to a neutronand vice versa. In a nucleus, beta decay changes both Z and N by one unit:Z −→ Z±1, N −→ N∓1, so that A = Z+N remains constant (A indicates themass number, Z the atomic number, and N the neutrons number). Thus betaradiation provides a convenient way for an unstable nucleus to ’slide’ down withconstant mass down to a more stable isobar. Refer to Table 1 for an overview.

These processes add a neutrino or antineutrino, marked by ν and ν, respec-tively. Alpha particles are emitted with sharp, well defined energies, equal tothe difference in mass-energy between the initial and final states (with smallrecoil corrections). Alpha particles connecting an initial and final state haveexactly the same kinetic energies. On the other hand, beta radiation has acontinuous distribution of energies, from zero up to an upper limit, which is

3

Table 1: Basic Beta Radiation Processes

Original Nucleon Nucleon prod. + radiated parti. Name of Processn −→ p + e− + ν Negative Beta Radiationp −→ n + e+ + ν Positive Beta Radiationn ←− p + e− + ν Orbital Electron Absorption

the deference between the initial and final energy state. Had the beta radiationbeen a two-body-decay process like the alpha decay (daughter-nucleus and ahelium nucleus) all the beta particles would have had a specific energy. But,empirically we find that all the emitted particles have smaller energy than whatwe would expect from calculations for two-body-decays, thus we conclude thatthe beta radiation process is a three-body decay process, in which a neutrino oran anti-neutrino 2 is involved, and gets the remaining energy. In the process ofnegative beta radiation it is the other particle - the antineutrino - which takesthe excessive energy. The neutrino is the third particle in the positive betaradiation process and the electron absorption process. Conservation of electriccharge requires that the neutrino will be electrically neutral.

1.3 Energy Loss of Radiation in a Medium

Bethe formula gives us the rate of energy loss of α-radiation within a medium:

−dE

dx=

4π

mec2

nz2

β2

(e2

4πε0

)2 [ln

(2mec

2β2

I (1− β2)

)− β2

]Where β = v

c , v is the velocity of the particle, c is the speed of light, ze isthe particle charge (measured in elementary charges), n is the electron densityof the target and I is the mean excitation potential of the target. For smallvelocities (β << 1), the energy loss decreases as 1/v2.

This rate of energy loss is called the stopping power. Notice how it is depen-dent upon the energy (β2) and not the place (x). This energy loss is the resultof Coulomb repulsion between the alpha particles and nuclei in the matter. Asthe alpha particles pass through the material, electrostatic force is exerted uponthem which results in energy loss.

1.4 Detection Instruments

In their basic principle of operation, most detectors of nuclear radiation fol-low similar characteristics: the radiation enters the detector, interacts with theatoms of the detector’s material (losing part / all of their energy), and release a

2Name given by Fermi.

4

large number of relatively low-energy electrons from their atomic orbits (ioniza-tion). These electrons are then collected and formed into a voltage or currentpulse for analysis by electronic circuitry. The specific choice of material dependson the type of radiation we are trying to detect and upon the information aboutthat radiation we are trying to gather. For our purpose - alpha & beta radiation- the sufficient thickness of the detector is less than 100µm for alpha, and lessthan 0.1−1mm for the beta. To measure the energy of radiation we should selecta detector in which the output pulse amplitude is proportional to the energy ofradiation - we must choose a material in which the number of released electronsis large, so that if we experience statistical fluctuations or fail to count a few, itdoes not substantially affect our ability to measure the energy.

In our experiment we used a silicon-based detector. We will first refer to sili-cone as a semi-conductor and emphasize some of its characteristics that concernus. A semiconductor is a material which has a small energy gap of about 1eV

(with respect to the conducting material). This energy gap is between the va-lence band and the conduction band. This characteristic enables (statistically)small amounts of electrons (∼ 10−9) to be thermally excited and get throughthe gap into the conduction band, leaving vacancy in the valence band - ’a hole’.The rest of the electrons are then migrated to compensate the instantaneouslynegative charged region, and thus the ’hole’ migrates in the valance band. Po-tentially dynamic properties of small energy gap materials are indicated by thismigration - we can control the flow of electrons through a certain region. Toenhance the control the inventers of the semiconductor ’doped’ the 4-valenceelectrons materials with 3 or 5-valence electron materials (Phosphorus, Arsenic,Antimony). This ’doping’ process is done to ensure getting donor states onthe energy gap, right under the conduction band and right above the valenceband. These characteristics enable us to get an intrinsic electric field withinthe connection region between the two types of materials - a depletion region.This region acts as a sort of ’parallel-plate capacitor’ in a way which takes theelectron and its respective ’hole’ which were created due to an impact of radia-tion on the depletion region, and accelerate it to the positive / negative ’plate’,respectivley. The total amount of electrons can be collected, which forms anelectric pulse. Other benefits of the depletion region is that we can control itssensitivity by activating on it a ’reverse bias’ (opposite voltage) that enlargesthe region that interacts with the radiation.

2 Apparatus

The experiments were performed inside the laboratory of the third year com-pound within the university (HUJI). Within the compound, we were allocated aroom to perform our experiment, and in this room two more experiments wereheld simultaneously, which did not deal with radioactivity. Aside to the com-pound, a separate, locked, cabin contained the radioactive source (Thorium-228)for the experiment. Within the room in which we performed the experimentthere were a plethora of instruments (we connected them in a fashion similar to

5

what Figure 1 exhibits):

• A PC computer system running Windows XP and with the spectrometrysoftware ”Maestro” installed. Also installed on the computer was a boardthat received analogue signal (pulses of voltage where the height of thepulse signifies the energy of the particle) and converted it to a digital one- a multi-channel analyzer. This board is called a PCA.

• Electronic circuitry:

– Pre-Amplifier - PA.

– Linear Amplifier - LA - ELSCINT / CAV-N-1 / Max 500V - we usedvoltages of 50V .

– Power Source - Stanford Research Systems PS310 / 1250V -25W /”High Voltage Power Supply”.

– A scope - Tektronix / TDS 210 / ”Two Channel Digital Real-timeOscilloscope”.

– Single Channel Selector - SCA - Ortec / 550A.

• A vacuum-able compartment that holds the radioactive source (a metalplate rich with radioactive isotopes) and has a built-in radioactivity-detectorof the semi-conductor type (made of Silicon). Thus the compartment, hadtwo ends, the one was used to vacuum it and remove pressure, and theother was an electric one, which outputted signal from the detector. Thewhole complex itself could be taken apart in order to put the source insideit.

• A system of pumps

– A mechanical-rotation pump - from 1atm to 0.1Torr.

– A diffusion pump - from 200Torr to 10−6Torr.

– Liquidized Nitrogen-cooled pump.

• An electric pressure-meter for which the error is not known - GRANVILLE-Phillips / Helix Technology Corporation / 275 Mini Convention.

• A series of tubes.

• Pressurized Nitrogen containers.

• A whiteboard for debriefings.

6

Figure 1: Connection of the devices used for measurements.

!"#$%&'(%)*+&,)"#,

-&".+)*/010"&

2)*/010"&

-3)*0#4

!"#$%&'5/"6,&%#06$'7%8

-%9"&'!%3&6"

-(2-"&$%#+/(%)*3,"&

3 Method

Our experiment spanned over the course of numerous sessions in the labora-tory. Although we attended to different features in each measurement, all themeasurements were done in a fairly similar manner.

First we had to obtain the radioactive source (Thorium-228), which waslocated in a cabin outside the laboratory compound. The source is held inside anair-conditioned compartment in order to prevent Radon gas from accumulatingin the room. Above the source a charged metal plate was put to attract ionsof radioactive isotopes. On the metal plate an equilibrium is achieved betweenthe decay of daughter isotopes and the creation of them by the parent isotopes.The equilibrium is achieved due to the voltage on the plate. Hence as long asthe plate is connected to voltage, it will always be ”charged” with daughter-isotopes of Thorium-228. So obtaining the radioactive source meant replacingthe metal plate above the radioactive source with an ”empty” one from an oldexperiment and using the ”fresh” one - a procedure done exclusively by ourprofessor. The metal plate was put inside a lead container (to protect fromradioactive pollution) and taken back to the experiment room. Once we hadthe radioactive source within the experiment room, we took it out of the leadcontainer and into the detector compartment. The source was placed as closeas possible to the detector (within the compartment) in order to avoid energyloss inside the compartment. The detector compartment was then attached toa tube connected to the pumps and thus we could create vacuum in it. Oncethe compartment had relatively negligible pressure (measured by an electricpressure-meter, we saw a pressure of about 1mTorr), we connected the electriccircuitry from the detector to the computer (or alternatively to the scope, fordiagnostic purposes) in a manner which will be elaborated upon later. Oncethe detector with its circuit was connected to the computer, we could produce

7

a histogram of how many particles hit the detector (counts) per specific energy,which was represented in arbitrary ”channels” - 2048 of them.

3.1 Calibration Session - November 9, 2006

The system had to be calibrated (at the beginning of each experiment) to cor-respond channels to physical energy units (keV in our case). The calibrationprocess was done by identifying the extreme peaks of counts in the histogram3

as either Polonium (for the right) or Bismuth (for the left, two peaks which needto be distinguished). Since the energy of the alpha-particles emitted by theseisotopes was known and published in the literature (a radioactivity chain map inthe halls of the laboratory compound), we could create a linear transformationbetween their channel position and their energy in keV . Then, we could see theactual energy of other peaks (which were not in the extreme right or left) andfind out from which isotopes they came from, since alpha particles have discreteand specific energy for each isotope they come from.

3.2 Half-Life Time of Alpha Radiation Session - Novem-ber 13, 2006

We performed the calibration process as described above, and then saved thehistogram on the computer. The capture duration was for five minutes (mea-sured with a wrist-watch) and there were five measurements made at intervalsof 20 minutes.

3.3 Stopping Power Session - November 20, 2006

This time, we followed a slightly different procedure in order to setup the system.Instead of placing the source as close as possible to the detector, within thedetector compartment, we placed it at some distance (≈ 8.2cm±0.5cm from themetal plate to the detector plate). We then hooked up the Nitrogen container tothe series of pumps in order to stream Nitrogen into the detector compartment,instead of creating maximum vacuum in it. We know what was the pressurewithin the compartment using the same electric pressure meter. Using dials, wecould change the pressure (or density of Nitrogen) inside the compartment.

So we made a series of captures of the histogram on the computer, eachat different pressure of Nitrogen (∼ 0, 70Torr, 103Torr, 121Torr, 172Torr,264Torr).

3.4 Beta Radiation Session - November 23, 2006

The beta radiation session was the most distinguishable from all the other ex-periments we have made so far, since we had to prepare the daughter-sourceourselves, inside the experiment room. Our professor obtained the original ra-dioactive metal plate from the Thorium-cabin and then we followed the same

3See Figure 2.

8

calibration procedure as described above. After we made sure that the systemwas working as before, we disconnected all the instruments, removed the vac-uum, and put a second metal plate with voltage above the original metal plate.The voltage is used to create an equilibrium so that we have a constant numberof isotopes on the second metal plate. This was used to acquire a secondary-daughter isotope (Bismuth-212). Since this secondary daughter isotope has arelatively short half-lifetime (∼ 3.5minutes), we had to act quickly, and we evenmade rehearsals prior to the actual procedure. Basically, now that we were in-terested in beta radiation rather than alpha radiation, the energy spectrum wascontinuous and thus there was no way to identify which isotope the beta radia-tion had originated from. Additionally, the energy range was much lower thanthat of the alpha particles, thus we had to narrow our band to lower energies.This was done by changing the windows of the single channel selector to takeonly low energies. We knew the limit by first examining the signal in the scope,and seeing two types of signals: One high, for the alpha particles, and another,low, for beta particles. We used a single channel selector in order to input abinary (digital) signal to the computer, instead of an analogue one. This wasdone because we were not interested in the energy levels of the beta particles(since we could not identify their levels with any specific isotope). We wereonly interested in the activity of the beta radiation within time. Thus whatwe saw on the computer screen was a histogram with a peak at the width ofone channel4. The number of counts in this channel indicated how many betaparticles arrived at the detector. An alternative method (which has also beendemonstrated to us) was just integrate the area below the histogram and getthe total number of counts for the whole histogram.

We wanted to see how the total number of counts for beta radiation changesin time. So after charging the secondary-daughter isotope (which radiates beta)and rapidly connecting all the instruments - this time without vacuum, sincebeta is not substantially absorbed in air - we registered the total number ofcounts for a given period of time, at short intervals of time. We did this about20 times, with two sets of measurements.

4 Results

4.1 Calibration Session - November 9, 2006

In the first stage, we were presented with a histogram on the screen, whichlooked a lot like Figure 2. We then were told that the extreme right peakwas alpha particles which resulted from decay of Polonium-212 with energyof 8.785MeV and the extreme left was Bismuth-212 which radiated with twoenergies of 6.051MeV & 6.09MeV . The results we found can be shown in Table2 and Figure 3.

4Actually there were approximately three channels, due to noise of the instruments.

9

Figure 2: First Histogram for Calibration - the left most peak is beta radiation,and the other peaks are alpha radiation. Below is a zoom of the first graph,with arrows directed to the two peaks of the Bismuth isotope.

0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0

0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

Coun

ts

C h a n n e l o f M a e s t r o P r o g r a m

1 0 0 00

2 0 0 0

4 0 0 0

6 0 0 0

Coun

ts

C h a n n e l o f M a e s t r o P r o g r a m

10

Table 2: First Calibration Process and identification of middle peaks

Name of Isotope Energy (MeV ) Corresponding ChannelLower Bismuth-212 6.051 812.7Upper Bismuth-212 6.09 813.34

Polonium-212 8.785 1179.57Lower Bismuth-211 6.294952 843.98Upper Bismuth-211 6.6355 890

Figure 3: Our results for the calibration process. As can be seen, we found thefollowing relationship between the energy E in MeV and the arbitrary channel:E(MeV ) = 0.00741 × Channel + 0.04953. Notice how for channel of 0, theenergy is not 0. We relate that to error in the calibration process and not to agenuine trait of the measuring system. From this formula, we found the extraenergy values in Table 2.

8 0 0 8 5 0 9 0 0 9 5 0 1 0 0 0 1 0 5 0 1 1 0 0 1 1 5 0 1 2 0 0

6 . 0

6 . 5

7 . 0

7 . 5

8 . 0

8 . 5

9 . 0

Energ

y (Me

V)

C h a n n e l ( 0 - 2 0 4 7 )

11

Table 3: First Decay of upper and lower Bismuth-211 in time.

Time Elap. (min) Lower Bismuth-211 (Net Cnts./5mins) Upper Bismuth-211 (Net Cnts/5mins)0 4536 1863220 2246 1511840 2102 1084560 1465 764182 917 5160

4.2 Half-Life of Alpha Radiation Time Session - Novem-ber 13, 2006

In this session, we were interested in the half-life time of the middle (two)peaks in our histogram (not Polonium and neither Bismuth), which, accordingto Table 2, we identified as Bismuth-211 with two discrete energie. We wereto compute the half-life time by seeing how the number of decays (which isin fact the number of alpha particles that arrive at the detector) behaves intime. The computer program we used, ”Maestro”, had a feature which couldcalculate an integral of the counts below a given peak (and it also identified thepeak beforehand). We relied on this feature in order to estimate the number ofdecays. We also noticed that the channel at which the peaks were positioneddid not move (neglecting minor fluctuations). Table 3 summarizes the resultsfrom this stage. From this table we were able to create fits for the decay (seeFigure 4 and 5).

4.2.1 Final Result

We arrived at the result that the half-life time for the lower Bismuth-211 34.398±6.28 minutes whereas for the upper Bismuth-211 it is 46.7± 3.38 minutes.

12

Figure 4: Decay of Lower Bismuth-211 alpha radiation in time.

0 2 0 4 0 6 0 8 05 5 76 3 47 1 27 8 98 6 69 4 31 0 2 01 0 9 7

1 3 0 61 5 1 51 7 2 51 9 3 42 1 4 32 3 5 32 5 6 22 7 7 22 9 8 13 5 5 04 1 1 94 6 8 8

Coun

ts

E l a p s e d T i m e ( M i n u t e s )

Figure 5: Decay of Upper Bismuth-211 alpha radiation in time.

0 2 0 4 0 6 0 8 0

3 5 5 04 1 1 94 6 8 85 2 5 75 8 2 76 3 9 66 9 6 57 5 3 48 1 0 39 6 5 0

1 1 1 9 71 2 7 4 41 4 2 9 11 5 8 3 81 7 3 8 51 8 9 3 2

Coun

ts

E l a p s e d T i m e ( M i n u t e s )

13

Table 4: Pressure vs. Energy for Stopping Power Session

Pressure (Torr) Polonium (keV) Upper-Bismuth (keV)0 8782.31 6090

71.9± 3 8279.66 5390.64103± 2.5 8042 5074.12121± 2.5 7962.09 4958.53172± 2.5 7579.56 4394.88264± 2.5 6383.24 3314.24

4.3 Stopping Power Session - November 20, 2006

Processing the results was somewhat tricky. We wanted to see the graph of Betheformula. But all we had was how the energy shifted downwards as the pressurein the compartment risen (see Figure 7). So we calculated the difference (∆)between the measurements, both in energy and in pressure, then we convertedthe units from pressure to distance (∆x = lρ0P/P0, where P0 is 760Torr, ρ0 =0.0125g/cm3, and l is the distance in the compartment5) in order to be withaccordance to the Bethe formula. We have done this for two of the peaks in thehistogram - the Polonium peak on the extreme right and the Bismuth (which isdivide to two) peak on the most left. The plots are shown in Figure 8 and 9.

5[∆x] = g/cm2

14

Figure 6: A plot of the width of peak of Polonium-212 (from half the height)versus the pressure in the sensor compartment (which was filled with Nitrogen).We interpreted the width of the peak as a measure for the variance of the energiesof the alpha particles. As can be seen, the variance rises as the pressure does,which means that as the compartment is filled with more Nitrogen atoms, moreof them scatter and collide the alpha particles and thus the increase in variance.

- 2 0 0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0

2

4

6

8

1 0

1 2

Width

from

half-p

eak o

f Polo

noium

(Cha

nnels

)

P r e s s u r e ( T o r r )

15

Figure 7: A plot of the energy of alpha particles emitted from Polonium-212versus the pressure in the sensor compartment (which was filled with Nitrogen).As can be seen, the energy decreases as there are more Nitrogen particles insidethe chamber.

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 06 5 0 0

7 0 0 0

7 5 0 0

8 0 0 0

8 5 0 0

9 0 0 0

Energ

y(Kev

)

P r e s s u r e ( T o r r )

16

Figure 8: Stopping power for alpha particles emitted from Polonium-212 com-pared with data from NIST.

6 8 0 0 7 0 0 0 7 2 0 0 7 4 0 0 7 6 0 0 7 8 0 0 8 0 0 0 8 2 0 0 8 4 0 02 8 03 0 03 2 03 4 03 6 03 8 04 0 04 2 04 4 04 6 04 8 05 0 05 2 05 4 05 6 05 8 06 0 06 2 0

N I S T D a t a O u r D a t a

-dE\dX

(Kev

*cm^2

\mg)

E n e r g y ( K e V )

17

Figure 9: Stopping power for alpha particles emitted from Bismuth-212 com-pared with data from NIST.

3 0 0 0 3 5 0 0 4 0 0 0 4 5 0 0 5 0 0 0 5 5 0 04 0 04 5 05 0 05 5 06 0 06 5 07 0 07 5 08 0 08 5 09 0 09 5 0

1 0 0 01 0 5 0

N I S T D a t a O u r D a t a

-dE\dX

(Kev

*cm^2

\mg)

E n e r g y ( K e v )

18

Table 5: First Set of Beta Decay in Time

Counts per Second Time Elapsed [Seconds]11.10 708.76 1607.79 2005.92 2405.65 2755.77 3105.41 3555.30 3804.11 4204.27 4553.86 4902.82 5202.91 5603.07 6002.27 6402.43 6751.66 7151.62 7501.76 8101.49 8451.87 885

4.4 Beta Radiation Session - November 23, 2006

We made two sets of measurements to see how the total counts of beta particlesdecays in time. We made two sets to enhance the level of exactness. A plotof the data is presented in Figures 10 and 11, for the first and second sets,respectively. From the slope of the lines we were able to extract the half-lifetime of the isotopes involved in the beta radiation process.

4.4.1 Final Results

In the first set, we found the half-life time to be equal to 265.27±10.62 seconds.On the other hand, in the second set, we found the half-life time to be equal246.64 ± 14.65 seconds. The fact that we got two different results in thesetwo sets is related to error in measurement and not to any physical shift inthe half-life time of the isotopes involved. We knew there were at least twoisotopes involved in the decay process, and the half-life time we measured is asuperposition of the two. Thus it is probable to find that we have two differentlines, one when most of the isotopes of the first kind are present, and anotherwhen they have all decayed and just the second type is present and radiating.

19

Table 6: Second set of Beta Decay in Time

Counts Per Second Time Elapsed [Seconds]5.41 904.29 1504.56 1755.12 1954.83 2153.43 2352.63 2653.69 2852.32 3053.20 3253.08 3453.07 3652.26 3852.59 4052.72 4252.33 4452.25 4651.50 4851.30 5051.77 5251.69 5451.13 5651.71 5851.60 6051.21 6250.85 6401.03 6750.57 6950.66 7151.04 7350.37 7500.75 7701.09 7850.75 8100.95 8500.84 8750.56 890

20

Table 7: Beta Decay Half-Life Time results for our two data sets.

Data Set Superpositioned t1/2[s] 1st t1/2[s] 2nd t1/2[s]1 265.27± 10.62 288.12± 42.39 60.34± 104.962 246.63± 14.65 230.06± 33.27 44.97± 89.35

Average 255.95 259.09 52.65

Figure 10: First set of beta radiation t1/2 measurement

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 00 . 1 3 5 3 4

0 . 3 6 7 8 8

1

2 . 7 1 8 2 8

7 . 3 8 9 0 6

2 0 . 0 8 5 5 4

Coun

ts pe

r Sec

ond

T i m e E l a p s e d ( S e c o n d s )

Closer examination of the linearization of Figure 10 or 11 indeed reveals thatthere are two slopes of two different straight lines. In order to better prove thispoint, we made a fit of the two data sets (of set 1 and set 2) for the functionn(t) = n1e

−λ1t + n2e−λ2t. Table 7 summarizes what we found.

21

Figure 11: Second set of beta radiation t1/2 measurement

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0

0 . 0 1 8 3 2

0 . 0 4 9 7 9

0 . 1 3 5 3 4

0 . 3 6 7 8 8

1

2 . 7 1 8 2 8

7 . 3 8 9 0 6

Coun

ts pe

r Sec

ond

T i m e E l a p s e d ( S e c o n d s )

22

5 Discussion

It is the purpose of the discussion section to compare the values we measuredwith those found in the literature. Then it would be adequate to explain, andfind possible reasons, for deviations from these literary values. Finally, someconclusions for future experiments or perhaps theoretical epiphanies can bepresented.

5.1 Bismuth-211 decay half-life times

According to the literature, the half-life times of the two decays of Bismuth-211are 2.17 minutes for the two energies. We arrived at 34.398± 6.28 minutes and46.7± 3.38 minutes. It would seem that because the half-life time for Bismuth-211 is so small (2.17 minutes), it would be naive of us to try to measure it from asample of its bigger grand-parent, the Thorium-228. Bismuth-211 is a duaghterisotope of Pb-211. The half life time of Pb-211 is 36.1 minutes - which resembleswhat we measured more closely. So, what happens is that Pb-211 controls thecreation of Bismuth-211 and since the half life time of Bismuth-211 is so small,we effectively measure the half life time of Pb-211. In this light, it would seemthat our results are sufficiently close to the literary values.

5.2 Stopping-Power of Alpha Particles

As can be seen from Figures 8 and 9, our results deviate from those given by theNIST group (see Figure 12), which we consider to be a reliable literary source.Our best hope to explain this behavior is to blame the pressure measurementswhich were done during the different phases of the experiment. Although thepressure meter is digital, we registered the pressure in the beginning of thecapture, and we did not make sure that the pressrue stayed constant during thefive whole minutes of the capturing process. It could be postulated that thepressure has changed dramatically and this is the source for the error in ourresults. It is also the only parameter that has the capacity to change duringthe measurements, since all the other parameters are given to us (since we aredealing with difference in energies and not with absolute energies) by a computerprogram. Notice how for high energies, the deviation from the NIST group datais smaller compared to the deviation in lower energies. Also notice that we haveone extremely deviant point, which even without comparing it to the NISTgroup data seems suspicious. We consider it to be an error in measurement ora typo.

23

Figure 12: Data taken from NIST for Stopping Power of alpha particles inNitrogen.

24

5.3 Beta Radiation half-life of Thallium-207 and Thallium-208

The two isotopes in the measurements that radiated with beta were Thallium-207 and Thallium-208. The literary values for the half-life time of these isotopesis 4.77 minutes and 3 minutes, respectively. When we tried to see the slope ofthe superposition of these decays, we found rather similar values (see Table 7- approximately 4.26 minutes). However, when we tried fitting to the formulan(t) = n1e

−λ1t+n2e−λ2t it generally failed, giving values of less than one minute

for one of the half-life times. We believe this is due to the freedom given to thefitting program, which can pick any combination of two numbers and closely fitthe data.

25

References

[1] W.R. Leo Techniques for Nuclear and Particle Physics Experiments 1987:Springer, Berlin and Heidelberg.

[2] G.F. Knoll Radiation Detection and Measurements 1989: Wiley.

[3] Kenneth S. Krane Introductory Nuclear Physics 1988: J. Wiley and Sons.

[4] I. Kaplan Nuclear Physics 1963: Addison Wesley.

[5] http://physics.nist.gov/PhysRefData/Star/Text/ASTAR.html

26