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Nuclear Decay and Gamma-ray Spectroscopy
This lab has two parts (one week each): I. Nuclear Decay and II.
spectroscopy.
Gamma-ray
I. Nuclear Decay
OBJECTIVE
To study the radioactive decay process and to gain familiarization with some
simple instrumentation and techniques of experimental nuclear physics.
BACKGROUND READING
1. Melissinos, Experiments in Modern Physics, (Academic Press, Second Edition)
2. Boas, Mathematical Methods in the Physical Sciences, (John Wiley and Sons, Second
Edition).
PLOTTING THE GEIGER PLATEAU
The detection of x-rays, -rays, -rays, -particles, and high energy particles
depends upon the detection of the ionizing effects which they produce. Many different
kinds of detectors have been invented to detect these ionizing radiations. Among these are
the Geiger counter, proportional counter, cloud chamber, bubble chamber, scintillation
counter, solid state detector, and multi-wire proportional counters. All of these detectors
depend for their operation either on the detection of the ions produced by the particles
themselves, such as is the case for high energy electrons, protons, etc., or on the detection
of the ions produced by the secondary particles as is the case for -rays and x-rays.
One of the most commonly used detectors used to detect nuclear radiation (alpha,
beta, and gamma rays) is the Geiger counter or the Geiger-Muller (G-M) counter. The
detection process in the Geiger tube is based on the ionizing effects of the radiation. All
three types of nuclear radiation are capable of ionizing a gas. The degree of ionization
depends on the energy of the radiation and the amount of radiation absorbed by the gas.
Most G-M tubes are not sensitive to alpha particles unless they possess very thin
windows. Beta particles (electrons and positrons) are detected quite easily while gamma
rays, being more penetrating and non ionizing will often pass through the tube with little
effect. G-M tubes will only detect about 2% of the gamma rays which pass through them.
The G-M tube used in this lab consists of a thin wire (anode) suspended along the
center axis of a metallic cylindrical tube (cathode). The probe has a potential difference
applied between the anode and cathode and is filled with a gas at low pressure. When
radiation enters the end window, it ionizes the gas producing ion pairs that are then
attracted to the electrodes. The motion of the ions to the electrodes constitutes an electric
current pulse which is subsequently detected and recorded.
The characteristics of the current pulse depend strongly on the voltage applied
across the electrodes of the tube. At low voltages, the pulses consist essentially of those
ions produced by the radiation and are quite small. As you increase the voltage, the ions
are accelerated sufficiently to produce additional ion pairs, causing an avalanche in the
high electric field near the center wire. At such potentials, the size of the pulses are much
larger, but proportional to the number of avalanches and thus to the original number of
ion pairs formed. Since the radiation expends approximately 32 eV per ion pair, the tubes
operating at such potential are known as proportional counters. Further increase in the
high voltage leads to the Geiger – Muller region. In this region, a single avalanche
produced by a single electron generates new avalanches so that the discharge spreads
along the whole counter. This process will stop when an ion sheath develops around the
central wire, reducing the field at the wire to such an extent that no further multiplication
can occur. This is known as quenching, and the gas in the tube facilitates this action. At
still higher voltages, the tube breaks down, developing arcs which destroy the tube.
In this lab, the tube is operated in the Geiger – Muller region. After such a large
pulse as is obtained in this region, the tube is inoperative for a short period of time (~ 100
– 500 microseconds). Any radiation passing through the tube during this time will not be
counted. Corrections for this need to be made only when operating at very high counting
rates.
Now is a good time to read Melissinos, to get the details on gaseous ionization
instruments.
PROCEDURE: Geiger Plateau
1. The instructor will discuss the general radiation safety procedures.
2. Connect the Geiger tube to the counter by means of the medium high voltage coaxial
cable. Before plugging in the counter to an ac outlet, familiarize yourself with the
controls, particularly the high voltage control. Make sure the high voltage control is
turned fully counter – clockwise (0 V or minimum voltage setting) and the counter is
turned off.
3. Plug in and turn on the counter. Place the radioactive source (Cobalt 60) about two
inches from the end of the Geiger tube with the source facing the tube. Allow it to
warm up for about 5 minutes.
4. Slowly increase the tube voltage by means of the high voltage control until the first
indication of counting is observed. Decrease the voltage about 50 volts. Observe and
record the number of counts per unit time at various voltages by increasing the
voltage in 25 or 50 volt steps.
It is important that you plot your data as you go along. This procedure often saves a
great deal of time in catching a poor procedure. Place error bars on each of the points.
5. In order to prevent continuous discharge and destruction of the tube, DO NOT
increase the voltage beyond the point where the count rate is more than 10 percent
above the plateau value. (It is better not to exceed 700 V.)
For all future experiments, you must use this counter and Geiger tube.
NUCLEAR DECAY
Any individual radioactive nucleus has associated with it a definite probability per
unit time that it will decay. This does not depend on measurable history of the nucleus or
the nature of the surrounding atoms. Thus, the process is thought to be purely random.
For a given sample of material, the total number of decays per unit time depends on the
probability of decay of each nucleus times the total number of radioactive atoms present.
This relationship is expressible as:
dN (t )
  N
dt
(1)
where N is the number of atoms and  is the decay constant. The solution of this well
known differential equation is
N (t )  N o e t
(2)
where No is the number of radioactive atoms in the sample at t=0 and N(t) is the number
at some later time t. What is usually measured is the number of decays per second or
better known as the activity. It follows from Equation (2) that
dN
   N o e  t    N
dt
dN
Activity  
 N  (N o ) e t
dt
(3)
(4)
The minus sign indicates that the number of unstable nuclei decreases with time.
If a counting device is positioned adjacent to a radioactive sample, it will have
some probability of detecting energetic particles produced in the radioactive decay
process. Thus the count rate observed, if all physical parameters of the apparatus affecting
the detection probability are held constant, will be proportional to N. In this way, N can
be observed as a function of time and the decay constant, , can be determined. Another
parameter commonly used to describe nuclear decay is the half life (t1/2). This is the time
required for one half of all the radioactive atoms in the sample to decay. From equation
(2), t1/2 can be found as follows:
N0
 N o e t1 / 2
2
N 
ln  0   ln( N o )  t1 / 2
 2 
ln 2
Half life  t1 / 2 
(5)

The mean life is given by

tmean  
dN
tdt
dt
,
(6)
1
tdN ,
N
(7)
dN
 dt dt
which can be written as
tmean  
and from Equation 3 we have
tmean   te t dt
(8)
Integrating this and using Equation 5 gives
tmean 
1


t1/ 2
0.692
(9)
The strength of the radioactive sample used in this course is less than 1 micro curie. This
is so weak that it is exempt from EPA licensing. You will observe a short lived isometric
state of barium 137 in this nuclear decay experiment. The sample will be separated from a
‘radio nuclide cow’ by elution. The cow contains Cs137 which is insoluble in the solution
used for separation. Cs137 decays by beta emission to Barium 137.
137
55
Cs13756mBa   
(10)
(m denotes a metastable state or isomeric state). The decay process leaves a substantial
fraction of Barium 137 in an excited isomeric state which then decays by gamma ray
emission to the ground state of Barium.
137 m
56
Ba137
56 Ba  
(11)
The half life of Ba137 is approximately 2.55 minutes. You will detect these gamma rays
with a Geiger counter.
PROCEDURE : Nuclear Decay
1. Set the voltage at the operating voltage as determined from Part A of the experiment.
2. With all radioactive sources removed from the vicinity of the apparatus, take a five
minute background count and record your result. Determine the background count
rate in counts per minute. This should be subtracted from subsequent measurements.
What are the source(s) of this background radiation?
3. Read the Operating Instructions for the Cs/Ba-137m Isotope Generator. Place a
watch glass under the radio nuclide cow and elute a few drops of radioactive barium
137 onto the filter paper. Place your sample under the Geiger tube immediately after
elution. Any delay will result in loss of accuracy. Why?
4. Start taking measurements using one minute intervals. Continue taking data at
regular intervals for at least 15 minutes.
5. Make a semilog plot of your data. Be sure to include error bars on your graph. What
errors are associated with the process of radioactive decay? (See An Introduction to
Error Analysis, John Taylor, University Science Books, 2nd Ed., 1997). By doing a
weighted fit, determine the half life from the graph. Be sure to discuss the origin of
the error bars and importance of weighted fit in your report. Compare this value with
the handbook value.
6. How is the half life related to the decay constant of a radioactive source?
7. Ba137m is a nuclear isomer of Ba137. Explain what this means.
II. Introduction to Gamma Ray Spectroscopy
In this laboratory, you will have chances to explore the essentials of gamma ray
spectroscopy using a Na I scintillation detector coupled to a multi-channel analyzer
(MCA). Manual to this experiment is at your station. Read Introduction and familiarize
yourself with health physics issues. You will perform the following experiments
described in the separate handout posted on blackboard.
Experiment #1 [Energy Calibration]: You will learn to calibrate the detector using a
standard gamma source.
[Note: First switch the power on, only then start the program. Set HV on. Sometimes
the program does not communicate with the instrument. Try to do Autocalibrate first
before doing actual calibration. It will bring HV on. The software in your lab is newer
than the one described in the manual. However, all the essentials are the same.
You will need to repeat calibration each time you switch the instrument o].
Experiment #2 [ Gamma Spectra of Common Sources & Identification of an Unknown
source] : Using your calibration, you will obtain gamma ray spectra of several sources
available in the laboratory (137Cs, 54Mn, and 60Co) and compare your results with
available data on these sources. You may skip p. 11 of this experiment.
Experiment #4: [ Compton Scattering]. You will study Compton Scattering as revealed
in the gamma ray spectrum of Cs 137. Skip addition of the lead sheet and p. 16.
Printouts of all experimental results including calibration should be included in your
report.
Optional: If time permits you are encouraged to do Experiments #3 ,#5 and #6 .
The Balmer Lines of Hydrogen
Purpose: To measure and interpret the Balmer line spectra series of hydrogen and determine the mass of
Deuterium atom.
Apparatus:
1. Ocean Optics USB4000 & HR 4000 Fiber
Optics Spectrometers
2. PC
3. Hydrogen/Deuterium spectrum tube
4. Mercury spectrum tube
5. Hydrogen Spectrum Tube
Introduction:
In 1885 Johann Balmer (a Swiss schoolteacher), succeeded in obtaining a simple relationship among
the wavelengths of the lines in the visible region of the hydrogen spectra:
2
 =   2n
(1)
where n = 3, 4, 5, . . .; n > 2
n -4
where λ = 364.25 nm is a constant which the series approaches as n -> . It is more convenient to
express them in terms of wave number (1/λ)
1
1
1
 = = R  2 – 2 

2 n 
where n = 3, 4, 5, . . .; n > 2
(2)
where R is the Rydberg constant for hydrogen and . Twenty-three years later, other series of the hydrogen
atom’s spectral lines were discovered. By 1924 five series had been discovered, and they are
Hydrogen Series of Spectral Lines
Discoverer (year)
Wavelength
nf
ni
Lyman (1916)
Ultraviolet
1
>1
Balmer (1885)
Visible, ultraviolet
2
>2
Paschen (1908)
Infrared
3
>3
Brackett (1922)
Infrared
4
>4
Pfund (1924)
Infrared
5
>5
Bohr theory of hydrogen atom, as well as quantum mechanics gives for the hydrogen lines,
 1 1
= R  2 – 2 

 n f ni 
1
where R =
2  2 me4
= 1.09737309 x 107 m-1
2
3
c h (4  0 )
(4)
where m and e are the mass and charge of the electron, c is the velocity of light, h is Planck’s constant, and
nf and ni are integers with nf < ni. The Bohr formula given above was derived assuming that the nucleus had infinite mass and does not move as the electron "orbits" about it. Taking into account that the electron and proton move about the center of mass, we replace the mass m of the electron by the reduced mass μ of the atomic system: = m m 1+ MH (5) where MH is the hydrogen nuclear mass. This value for the Rydberg constant agrees extremely well with experiment and is given by RH = MH 7 -1 R = 1.09677576 10 m MH +m (6) It was discovered that many spectral lines possess an aggregate of very fine lines which could not explained This can be explained with existing theory based on electronic structure of the atom. Systematic studies reveled that there are two kinds of hyperfine structure. One kind arises from the presence of several isotopic nuclei for a given chemical element and this is known as isotope shift. For light atoms such as hydrogen, the isotope shift appears to arise from simple differences in the effects of nuclear motion. For heavy atom, the isotope shifts are found, in general, to be proportional to the differences in atomic mass. The second kind of hyperfine shift was first explained by Pauli in 1924 as due to the fact that nucleus possess an angular momentum and an associated magnetic moment and it interacts with the outer electrons. We are only interested in the isotope shift. In the case of hydrogen, the isotope shift was used as a guide by Urey and his collaborators in the discovery of heavy hydrogen H2 or deuterium, D. The Rydberg constant for deuterium is given by RD = MD R MD+m where MD is the deuterium mass. H-D Spectra 2 (7) Apparatus: Learn about USB4000 and HR 4000 Fiber Optics Spectrometers from Installation and Operation Manuals (Manuals are at your work station and on the BB site). The schematics and principle of operation of the spectrometers should be included in your lab report. The Geissler atomic hydrogen gas discharge tube has an atmosphere of pure water vapor which dissociates into hydrogen ions and atoms. The H2 molecules which are also formed during the discharge are continuously purged from the lamp and converted to water vapor by a special cartridge inside the electrodes. You will also use a special Geissler tube containing 50 % hydrogen and 50 % deuterium. The other apparatus used includes a mercury discharge tube, associated electronics and computer. UV LIGHT WARNING DO NOT STARE AT THE MERCURY OR HYDROGEN LIGHT! A. Determining the Wavelengths of Balmer Series (USB4000 Spectrometer) Before you begin, check the calibration coefficients of the USB400 spectrometer to make sure that these have the factory set values. If the values are different, please contact the instructor before beginning 1. Run the Ocean View software. Familiarize yourself with its operation. [Refer to the manual and understand the controls and settings. You will collect data in the QuickView mode]. 2. Set up a hydrogen tube. Record its spectrum using the USB 4000 spectrometer. Also, record the spectra of the Deuterium tube and the Hydrogen-Deuterium mix. Examine if there are any differences. [Steps 2 through 7 need to be carried out only for the hydrogen spectrum]. 2. Determine the wavelength of all the lines observed in the wavelength region from 380nm to 660nm. Compare your results with the accepted values listed in Handbook of chemistry and Physics. 3. Use Equation 2 to determine the Rydberg RH for each of the lines of the Balmer series. Take an average of your RH (air) values, and correct it to vacuum using the index of refraction of air (nair = 1.000292): (8) RH (vacuum)= nair RH (air) 4. Also plot the wave number versus n-2. From the slope determine the Rydberg constant. Compare wuth H-D Spectra 3 accepted value. 5. Calculate the Ionization Potential of hydrogen atom using your Ryderg constant value. Compare with the accepted value. 6. From the y-intercept determine the Balmer series limit. 7. Compare the calculated values with the accepted values. B. Calibration of USB 4000 Spectrometer using the Mercury-Argon source [ Important: do not calibrate the HR 4000 spectrometer]. 1. Set up the Mercury- Argon source and position the optical fiber for light collection and measurement using the USB4000 spectrometer. Note that there is a special optical fiber to be used for calibration. 3. Familiarize yourself with the calibration method and steps 4. Record the Mercury-Argon spectrum after optimizing the parameters 5. Record the spectrum of the pure Mercury source. Tabulate and compare the observed values and listed values in the CRC handbook. Estimate the error % 6. Record the spectrum of the hydrogen source. Tabulate and compare the observed values and listed values in the CRC handbook. Estimate the error %. 7. Record the spectrum of the Hydrogen-Deuterium source. 6. Calibrate the spectrometer using the listed values of spectral lines. Be sure to save your calibration coefficients and report these. 7. Repeat steps 5 and 6. Compare the Mercury and Hydrogen spectra before and after Calibration. Explain any differences or lack thereof. [The calibration procedure and results must be discussed in your report. Comment on any differences you observe between the two spectrometers including possible reasons]. 8. Restore the calibration coefficients to factory-set values. C. Mass of Deuterium Atom. [ You will use HR 4000 for this experiment]. 1. Remove the hydrogen tube and replace it with the Deuterium tube. Record its spectrum. To compare H spectrum and D spectrum, they should be plotted on the same graph (lines should have H-D Spectra 4 similar intensities). To determine the exact position of the lines, you should zoom on each line separately and include these data in your report. Do you observe the shift of the lines? 2. Repeat (1) with the tube containing Hydrogen-Deuterium mixture. 3. Compare results in (2) with spectra you obtained for Hydrogen-Deuterium mix with USB 4000. Explain any differences or lack thereof using your information on how the two spectrometers differ. 3. For any given line of the series, the isotope shift (λH. - λD) may be written as MD -1 H - D = M H M D +1 D m (9) where m, MH, MD are the masses of the electron, proton, and deuteron, respectively. From your data compute MD / MH, the ratio of Deuterium/Hydrogen masses. Compare with the expected value. Do this for both (1) and (2). [ Equation-9 must be derived in the theory section of your report]. 3. Show that if the atomic masses of H and D are known, then the mass of the electron is given by m= M H M D  D - H M D H - M H  D (10) ... 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