7/06 Radioactive Decay

RADIOACTIVE DECAY

About this lab

An unstable, radioactive nucleus of a particular type has a characteristic “lifetime”, expressed as mean life τ, or as half life T1/2 . Since such nuclei decay independently of one another, for an ensemble of similar nuclei one half of the initial “parent” nuclei can be expected to decay into “daughters” in the half life (but only on the average), and one half of those remaining parents again in the next half life, etc., etc. The sum of parents and daughters remains constant (or parents + daughters + granddaughters etc., if the daughter is also unstable).

Thus, a radioactive nucleus has a lifetime expectancy very different than do humans. For a human, the expectancy depends on the length of previous life. Not so for the radioactive nucleus, as long as it still “lives”, its life expectancy is still the same – it is not “used up”, as for humans. If a radioactive nucleus with a half life expectancy of 100 years happens (improbably) to have survived for 10,000 years, it still has a expectancy of 100 years.

The situation resembles that of a race of individuals that, once born, live forever without change, except for one randomly occurring infection which kill instantly. For a group of such individuals, the length of previous life would have no bearing on further life expectancy. The size of that selected group would diminish exponentially, with a characteristic mean life. For any individual member, only the probability of death in the following year is statistically predictable, and it is the same for any starting time. For the entire group, the fraction that will die in the next year is similarly predictable, but fluctuations about that prediction must be expected, due to the random nature of the process.

The “lifetime” of an unstable nucleus expresses a probability, not a certainty – it is a statistical quantity. As with many statistical quantities, fluctuations about the mean must occur, and we must expect to observe them.

Apparatus: Radioactive sources (long and short-lived), Geiger counter and tray holder, Timer/Counter (only used to power Geiger counter, not for counting or timing), computer, Logger Pro 3 data acquisition program, LabPro data interface,Vernier LabPro, Digital Adapter DG-BTD + RCA-stereo plug.

References: Cutnell & Johnson: Physics, 6th Sections 31.4 – 31.10Serway & Beichner: Physics for --- 5th v2: Sections 44.5 – 44.7

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Introduction

Figure 1 Three principal types of natural radioactivity, two charged, one uncharged..

We will be concerned directly with beta and gamma detection, not alpha. Our situation involves 1) a long lived (~ 30 years) parent (137Cs) which emits a beta ray, producing 2) a short lived excited state of daughter 137Ba* which emits a gamma ray to produce 3) stable granddaughter 137Ba, in its ground (lowest energy) state. It is necessary to separate the barium from the parent cesium, in order to stop replenishment of 137Ba * while we are trying to observe the decay.

(137Ba* then replenishes in the depleted cesium source, approaching close to equilibrium in around six short half lives of 137Ba*.)

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Figure 2 Exponential decay of radioactive daughter after separation from long lived radioactive parent. Regrowth of daughter in parental environment.

These curves have the same form as discharge/charge curves of a capacitor through a resistor.

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Figure 3 Statistical fluctuations in the random decay process for 1 second time intervals

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Figure 4 The naturally occurring 238U decay chain, terminating on stable 206Pb. Alpha and beta decay steps are involved. Some intermediate isotopes can branch in either direction, by alpha or beta emission.

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Figure 5 Lifetimes of the 238U decay chain and some principal members of the naturally occurring radioactive decay chain, beginning with uranium 238 and ending with lead 206.

All members have lifetimes much shorter than the parent 238U, leading to “secular equilibrium”, in which a the number of short lived daughters remains ~ constant due to constant replenishment. The result is that the daughter's apparent lifetime in the parental environment is that of the parent, i.e. long.

But, if the daughter is separated from the feeding parent, so there is no longer replenishment, the much shorter, true lifetime is exhibited.

This is also the situation with our chain: 137Cs –> 137Ba* -> 137Ba.

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Figure 6 Decay of parent 238U and growth of ultimate daughter 206Pb. Time step: 1e7 .

Intermediate progeny are in secular (time) equilibrium with the parent. Ratios offer dating possibilities, given knowledge of lifetimes. Scale is logarithmic.

http://www.mines.utah.edu/~ggapps/radiation/radiation.html

We will observe transitions in the short three-member chain below, involving:

1) A long-lived unstable parent 137Cs nucleus (beta emitter), and

2) A short-lived unstable daughter (half-life on the order of minutes) 137 Ba* nucleus (gamma emitter) (* denotes excited state), which we will separate in the lab from the parent 137Cs.

3) A stable granddaughter 137Ba ground (lowest energy) state.

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Source properties

The first radioactive source (beta ray emitting 137Cs) comes in a sealed plastic disk, mounted on an aluminum rectangle (see picture below):

Figure 7 A long-lived radioactive 137 cs source A thin "window" permits escape of many of the beta particles emitted in the decay of the 137Cs nuclei. These can enter the thin-windowed Geiger counter.

The second radioactivity observed is from 137Ba*, the daughter of the beta emitting parent 137Cs . 137Ba*, where “*” means “excited state of ”, emits gamma rays, which can easily enter the Geiger counter (gammas are uncharged photons) and, in some cases, interact with the gas atoms to release a charged atomic electron. . The 137Ba* daughter co-exists with the 137Cs parent, dying quickly and being replaced. The daughter will be stripped out chemically (no further replacement) in the lab by “milking” , using a mild HCl solution. The extracted liquid is then used as your radioactive sample (see extraction technique below).

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Figure 8 “Milking” the long-lived radioactive parent to separate the short-lived radioactive child.

(The deprived parent will make more daughters in the source barrel; substantial replacement will take around six short lives. Subsequently, birth and death of daughters is in balance, so the net number of daughters remains constant. (In strict theory, this only occurs after infinite time.) See growth curve in Figure 2 above.)

Figure 9 Geiger Counter tray with sample holder in top slot.

Use second slot for statistics measurements; use top for decay measurement.

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Geiger counter functioning

The detector, shown above, is a Geiger counter – a gas-filled cylinder with an voltage applied between an insulated, axial center wire and the outer metal conductor. The wire is +, relative to the tube, so primary electrons released by ionizing radiation drift toward the wire.. The field is large near the wire. If sufficient voltage is applied, an approaching electron gains enough energy in one mean free path (distance between collision with gas molecules) ) near the wire to ionize a molecule, releasing secondary electrons. An avalanche of electrons thus occurs near the wire, finally stopped by a positive ion sheath, which slowly drifts in the opposite direction (toward the outer conducting cylinder). The end result is a large voltage pulse on the wire, of size independent of the number of original primary electrons – all memory of the triggering electrons from initial interaction betwen gamma ray and a gas atom is lost and output pulses are all (more or less) the same size.

This "gas gain" makes Geiger counters cheap and reliable for use as radiation monitors. But the loss of information about the primary, initiating interaction is sometimes a handicap, for instance in monitoring for nuclear material smuggling by terrorists.

(At lower applied voltages there is similar “gas multiplication”, but initial memory is retained and the final pulse is proportional to the number of primary electrons. This operational mode is called proportional.)

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Figure 10 Geiger counter with radioactive source and Lab Pro data interface to Logger Pro software.

Characteristics of Radioactivity

We will first observe the statistical character (Gaussian Probability Distribution) of nuclear radiation, using a long-lived source of radioactive 137Cs. Then we will determine the decay constant/half life (exponential decay ) of the short-lived 137Cs daughter 137Ba* (milked from the radioactive parent 137Cs): a parent – daughter – granddaughter situation (see Appendix).

Gaussian distribution A long-lived source (e.g. 137Cs, 60Co) will decay negligibly during a few hours. Nevertheless, the counts observed during equal sampling intervals can fluctuate substantially due to the statistical (random) nature of decay processes.

If the counts per interval are more than a few tens, the spread in counts obtained in similar individual measurements will be very closely Gaussian, with standard deviation about equal to the square root of the mean. Thus, the size of the fluctuations will grow as the square root of the mean value (i.e., as the square root of the counting interval, for fixed rate), but the percentage fluctuations will decrease as the inverse. Study Figures 1 and 2. Note the approximate equality among std dev, sqrt(mean) and width (Gaussian fit C parameter) of the distribution histogram. Exact equality of sqrt and std dev is not to be expected, statistically, and the bin size chosen for the histogram can affect the fit.

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Figure 11 Statistical fluctuations in counting rate for 4 second time intervals

Note that the standard deviation of the upper curve, the Gaussian "C" parameter in the lower fit and the square root of the mean have similar (not identical) values.

“Lifetime” for Quantum Systems

As discussed above, in contrast to human experience, the lifetime expectancy of a radioactive system does not depend on how long it has already lived since formation – life expectancy is not “used up”. And the rate of decay is proportional to the number of surviving parents. It follows that the number of remaining parents decreases exponentially and, therefore, so does the rate of decay which we actually measure:

R = R0 e –λ t or, equivalently, R0 e – t /τ ( τ = mean life = 1/λ ).

An exponential curve-fit to the curve of rate vs. time will give the decay constant λ , and thus also its inverse, the mean lifetime τ (tau). Half life is sometimes used instead of τ : T1/2 = τ ln(2) = 0.693 τ. (A “third life” would be T 1/3 = τ ln(3), etc.)

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Procedure

Part A – Fluctuations: Gaussian Distribution of Counts

Open the Logger Pro 3.3 file Statistics of Radioactivity.cmbl . The parameters you will vary are Experiment Length and Count Interval. Radiation Counts will display the number of hits the Geiger Counter has registered in the last Count Interval. Experiment Length determines for how many of these intervals the software should take data. For example, if Count Interval is set to 4 seconds and Experiment Length 360 seconds, there will be 90 data pairs (Time, Radiation) in the Table, each corresponding to the number of pulses from the Geiger counter received in a 4 second time interval. After you press the Collect button, the software will begin to collect data. When the Experiment Length is reached, the software stops gathering data.

For this Part A your radiation rates should fluctuate around a mean value through the experiment (the long-lived 137Cs source rate is essentially constant over one lab period).

(For part B your radiation rates will drop during the experiment (137Ba* source decaying).

In Experiment: Data Collection set Count Interval = 1 second, Experiment Length = 360 seconds

1. Place a long-lived source in the top slot. Observe arrow direction of entry – placement is not centered. (Some counters may suffer counting rate losses at the higher rates encountered with closer placement.) You can start collecting data anytime by pressing the Collect button. Do not disturb the setup during the experiment.

2. After the experiment is finished, your data tables should have 360 sets of data pairs, plus corresponding derived (calculated) quantities. Examine all the graphs and the histogram.

3. For the time series graph, Analyze: Statistics.

4. For the histogram, vary the bin size (double click on the hist to set) to get a decent display. Make big bins (few bars) to see the peak, then narrow bins if desired. It can be difficult to recognize any peak with the initial display. Analyze: Curve Fit: Gaussian. You might need to do an initial manual fit to provide the Auto fit with good starting parameters for its optimizing search procedure. See Figure 11.

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If you need a manual start to the fit, input estimated values for A (maximum height), B (center of peak) and C (width), D (vertical offset). Adjust these parameters for visual fit. Then switch to automatic and Try It.

If the D parameter remains, the auto fit can sometimes do really stupid things, such as finding a large positive A and a large negative D, with the difference being around your manual fit starting value for A, or giving a horizontal line fit. If so, try getting rid of the D parameter, by:

Define function - choose Gaussian, then remove the D parameter (vertical offset). Manual fit, switch to auto and Try It.

Save. Print graph. Report stat quantities, Gaussian fit width parameter C, and square root of the mean value.

5. Don't move the source! Reset the Experiment: Count Interval 4 seconds, Experiment Length 360 seconds. Collect. Examine as before. Save. Print graph. Report results as before.

Compare 1 second and 4 second run quantities. Are the fluctuations larger for four second runs? Are the percentage fluctuations (relative to the mean value) larger for four second runs?

Part B - Lifetime Measurement

Open the Logger Pro 3 file Radioactive Decay.cmbl.

In the Experiment file: Data Collection, set the experiment parameters:

Count Interval = 20 seconds, Experiment Length = 1800 seconds (30 minutes)

Remove any nearby Cs 137 long-lived source - you only want the radiation from the short lived source.

1. When you have read all of Part B instructions and are ready to perform the experiment, get the 137Ba* sample from your TA, and insert in top slot. (Rates will probably not be excessive.) Insert the tray in the direction of the arrow, since the sample tub is not exactly centered.

2. Start taking data by clicking the Collect button. If you get fewer than 25 counts or so initially (20 second interval), consult your instructor as to whether you should wait for another source dispensation after the Cs-Ba source (small white barrel) re-equilibrates. (See regrowth curve for 137 Ba, Figure 2.) Leave the apparatus undisturbed for 30 minutes or six half lives.

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3. When data accumulation has ended, fit the decay curve to an exponential decay + constant background (Analyze: Curve Fit, Natural Exponent). From the best fit parameters, calculate τ (tau) and T½ (half life, = τ ln2). (For a fit function of the form exp(-C*t), C is the inverse of the mean life: τ = 1/C, and the % error in τ is the same as the % error in C.) Annotate the decay graph with these parameters. Report them, with errors. Compare your experimental mean life with the accepted value of 225 seconds.

NOTE THAT THE COUNT RATE NEVER DROPS TO ZERO, DUE TO BACKGROUND RADIATION, SOME LEAKAGE OF 137Cs SOURCE RADIATION, COSMIC RAYS,NATURAL RADIATION IN WALLS, FLOOR, ETC).

4. Dump sample in sink; rinse tray and hands.

Report Enter your data in the Report and answer any questions. Attach graphs.

Appendix

Nuclear radioactivity is a random process, obeying a statistical law, on the average:

Eq. 1 dP/dt = - λP where P = number of remaining unstable parents.

For every parent P death, a daughter nucleus D is born:

dD/dt = -dPdt = + λP (where dP is negative, since the # of P's decreases).

The solution of this simple differential equation is

Eq. 2 P = P0 e – λ t = P0 e -t / τ ( τ = 1/λ = mean life) where

dD/dt = λ P0 e –λ t .

Since each death/birth is accompanied by radiation (which is what we will observe; we won't count P's or D's directly) the radiation rate (signaling decay of daughter 137Ba* and birth of a granddaughter 137Ba) is

Eq. 3 R = λ P0 e – λ t = R0 e – λ t Daughter decay rate, = granddaughter birth rate

Exponential fit to the slope of the rate vs. time curve will give the decay constant λ, and thence its inverse, the mean lifetime τ (tau). Half life is sometimes used instead of τ :

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T1/2 = τ ln(2) = 0.693 τ.

The lifetime measurement involves a daughter which is also radioactive: a parent – daughter – granddaughter situation. The daughter is very short-lived, relative to the parent. In that case, in a depleted parental environment, daughters quickly build up until daughter production (by death of parents, at essentially constant rate) equals daughter death rate (by decay to granddaughter). This is called secular (i.e. time) equilibrium. The buildup involves the same daughter time constant λ as daughter decay (i.e., exp(- λdaughter t). Daughter buildup in a depleted parental environment is proportional to

Eq. 4 1−e _ t Daughter regrowth after depletion

There is a practical aspect. After the instructor separates the 137Ba * daughter out of the 137Cs parent source with a weak hydrochloric acid solution and dispenses a few samples for 137Ba* lifetime determination, he or she must wait for several 137Ba* half lives (10 – 15 minutes) before further sample dispensing, while the daughter again comes to secular equilibrium with its parent in the 137Cs source.

Natural radiation comes from naturally occurring unstable nuclei of lifetime comparable to that of the earth (e.g., 40K, 238U, 235U) or from unstable nuclei recently produced in the atmosphere by “cosmic rays”(e.g. 14C).

Standard radiation types are:

alpha (α): 4 He nucleus , 2 protons and 2 neutrons, A = 4, Z = 2,

beta(β, + or -): Identical to an atomic electron , but non pre-existing,

gamma (γ): EM radiation photon, usually of much greater energy than an atomic transition photon.

In addition the neutron (n) a nuclear constituent (A = 1, Z = 0) is sometimes a secondary product of natural alpha decay. Neutrons are produced copiously in fission reactors (along with α, β and γ's) , where they keep the “chain” going, easily penetrating a fissile nucleus such as 235

U or 239Pu, because the neutron is uncharged and therefore not repelled by the positive nuclear charge, as a proton or alpha particle would be..

The reactor-produced 13Cs has a half life of 30 years. It can decay (by β− emission) either to the stable ground (lowest energy) state of daughter 137Ba or (more often, also with lower energy β−

emission) to a short-lived (a few minutes) excited state (denoted 137 Ba* ). This excited state decays to the 137Ba ground state with emission of an (uncharged) gamma ray.

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______________________________________________________

Pioneer researchers of naturally occurring radioactivity included Henri Becquerel and Marie (Maria Sklodowska) and Pierre Curie. Albert Einstein said of Marie:

"Marie Curie is, of all celebrated beings, the one whom fame has not corrupted."

She was fortunate in a happy marriage and partnership with Pierre Curie, terminated untimely. Pierre worked with his wife Marie Curie in isolating polonium and radium. They were the first to use the term 'radioactivity', and were pioneers in its study. Their work, including Marie's celebrated doctoral work, made use of a sensitive piezoelectric electrometer constructed by Pierre and his brother Jacques.

Pierre and one of his students made the first discovery of nuclear energy, by identifying the continuous emission of heat from radium particles. He also investigated the radiation emissions of radioactive substances, and through the use of magnetic fields was able to show that some of the emissions were positively charged, some were negative and some were neutral. These correspond to alpha, beta and gamma radiation.

Marie Curie

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Marie Curie, one of the few people to win two Nobel Prizes in different fields, was one of the most significant researchers of radiation and its effects as a pioneer of radiology. Until her granddaughter recently had them decontaminated her notes were radioactive.

Marie Curie (Maria Skłodowska-Curie, November 7, 1867 – July 4, 1934), (Dolega coat of arms) was a Polish-born French chemist and pioneer in the early field of radiology and a two-time Nobel laureate. She founded the Curie Institutes in Paris and in Warsaw.

Biography

Born in Warsaw, Poland, her first years were sorrowful ones, marked by the death of her sister and, four years later, her mother. She was notable for her diligent work ethic, neglecting even food and sleep to study. After graduating from high school, she suffered a mental breakdown for a year. Due to her gender, she was not allowed admission into any Russian or Polish universities so she worked as a governess for several years. Eventually, with the monetary assistance of her elder sister, she moved to Paris and studied chemistry and physics at the Sorbonne, where she became the first woman to teach.

At the Sorbonne she met and married another instructor, Pierre Curie. Together they studied radioactive materials, particularly the uranium ore pitchblende, which had the curious property of being more radioactive than the uranium extracted from it. By 1898 they deduced a logical explanation: that the pitchblende contained traces of some unknown radioactive component which was far more radioactive than uranium; thus on December 26th Marie Curie announced the existence of this new substance.

Over several years of unceasing labour they refined several tons of pitchblende, progressively concentrating the radioactive components, and eventually isolated initially the chloride salts (refining radium chloride on April 20, 1902) and then two new chemical elements. The first they named polonium after Marie's native country, and the other was named radium from its intense radioactivity.

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Nobel Prize Diploma

Together with Pierre Curie and Henri Becquerel, she was awarded the Nobel Prize in Physics, 1903: "in recognition of the extraordinary services they have rendered by their joint researches on the radiation phenomena discovered by Professor Henri Becquerel". She was the first woman to be awarded a Nobel Prize.

Eight years later, she received the Nobel Prize in Chemistry, 1911 "in recognition of her services to the advancement of chemistry by the discovery of the elements radium and polonium, by the isolation of radium and the study of the nature and compounds of this remarkable element". In an unusual move, Curie intentionally did not patent the radium isolation process, instead leaving it open so the scientific community could research unhindered.

She was the first person to win or share two Nobel Prizes. She is one of only two people who has been awarded a Nobel Prize in two different fields, the other being Linus Pauling.

Historical 20 000 złoty banknote of Poland with face of Maria Skłodowska

After her husband's death, she had an affair with physicist Paul Langevin, a married man who had left his wife, which resulted in a press scandal. Despite her notoriety as an honored scientist working for France, the public's attitude to the scandal tended towards xenophobia—she was a foreigner, from an unknown land (Poland was still referred to as a geographical area, under the Russian Tsar), an area known to have a significant Jewish population (Marie was an atheist, raised a Catholic, but that didn't seem to matter). France at the time was still reeling from the effects of the Dreyfus affair, so the scandal's effect on the public was all the more acute. It is a strange coincidence that Paul Langevin's grandson Michel later married her granddaughter Hélène Langevin-Joliot.

During World War I, she pushed for the use of mobile radiography units for the treatment of wounded soldiers. These units were powered using tubes of radium emanation, a colorless, radioactive gas given off by radium, later to be identified as radon. Marie personally provided the tubes, milked from the radium she purified. Promptly after the

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war started, she cashed in her and her husband's gold Nobel Prize Medals for the war effort.

In 1921, she did a tour of the United States, where she was welcomed triumphantly, to raise funds for research on radium.

In her later years, she was disappointed by the myriad of physicians and makers of cosmetics who used radioactive material without precautions.

Her death near Sallanches, France in 1934 was from leukemia, almost certainly due to her massive exposure to radiation in her work.

Her elder daughter, Irène Joliot-Curie, won a Nobel Prize for Chemistry in 1935, the year after Marie Curie's death. Her younger daughter, Eve Curie, wrote her biography Madame Curie after her death.

In 1995, Madame Curie was the first woman laid to rest under the famous dome of The Panthéon in Paris on her own merits. There is a 1943 U. S. Oscar-nominated film based on it. An extremely ahistorical Marie Curie appears as a character in the comedy Young Einstein by Yahoo Serious.

Curie's picture was on the Polish inflationary late-1980s 20,000-zloty banknote. Her picture also appeared on the French 500 franc note and on stamps and coins.

Element 96 Curium (Cm) was named in her and Pierre's honour.

From Wikipedia, the free encyclopedia.