Before we start we need to reassure all parents, carers and neighbours of Rooks Heath that the radioactive sources used in schools are not dangerous. There are rules and regulations that have to be abided by mainly because some young people can be a bit silly and swallowing an alpha source won’t do you much good, but then neither will swallowing lots of other things.
All schools should have a radioactivity supervisor and at Rooks Heath this is Mrs Hare. There should also be a radioactivity adviser and ours are provided by cleapss.
Even though the school radioactive sources are not dangerous we abide by the rules because it enables students to learn about the sort of rules that have to be carried out with dangerous sources used in research, industry and medicine.
Before we purchased the sources a representative of cleapss came to check that we had everything in place to store them.
The sources are kept in a securely locked cabinet which can only be accessed by a member of the science staff and it is well away from the work space of any member of staff or student. The cabinet has the little trefoil sign on it stating “Radioactive material Authorised users only”.
When radioactive sources are used in research, industry and medicine. The people using them have to wear special film badges.
In schools this isn’t necessary but we do record who is using the sources and we do record how long they are using the sources in a log book.
Year 7 to year 11 students cannot handle the sources directly but at Rooks Heath they can now watch experiments that show the properties of the different types of radioactivity and GCSE students can now watch an experiment that shows how radioactive sources decay.
The best bit of having radioactive sources at Rooks Heath is that we in the sixth from can now do actual experiments rather than relying on simulations because we are allowed to handle the sources.
All students are given the rules regarding the use of radioactive sources whether they can handle them or not.
We use the most common type of sealed source which is sintered into a metal foil and secured at the base of a metal cup by a circlip. The open end of the cup is covered with wire mesh. It has a stem for handling and mounting. Details of the radionuclide and original activity are stamped on the back of the cup, next to the stem. A serial number is engraved there too. Cup sources are supplied in a small lead pot with a lead lid, inside a suitably labelled wooden container as shown above.
The source must be kept in its container and away from the other sources just prior to using it in an experiment. The source must not be handled directly but must be moved into place with very long tweezers. This ensures that the source is kept well away from the body. The source must not be pointed towards anybody.
We also use a protactinium generator to enable the half life of protactinium to be investigated.
This can be handled safely providing the lid doesn’t become loose or removed. It is a sealed, thin-walled fluorinated plastic bottle containing an aqueous solution of acidified uranyl(VI) nitrate beneath an organic solvent.
Before any radioactivity experiments are carried out a background count must be taken. This is a measure of background radiation. Background radiation is low level radioactivity/ionising radiation that is around us all the time.
People living in areas with lots of or mineralised sands receive more terrestrial radiation than others, while people living or working at high altitudes receive more cosmic radiation. A lot of our natural exposure is due to radon, a gas which seeps from the Earth’s crust and is present in the air we breathe.
Most human beings do get quite worried about the topic of radiation especially if they are living next to a nuclear power station but we do need some perspective. Bananas are radioactive because they contain radioactive potassium. Brazil nuts have a thousand times more radium (a radioactive element) than any other food item, and in some countries they actually dry herbs and spices by irradiation to counter bacteria, germination and spoilage. There’s thorium in your microwave oven and americium in your smoke detector.
Elsewhere in the house, cat litter, cigarettes, granite and brick are all actively radiating you. Always and forever, radiation is both raining down on you from the skies and floating up at you from our bedrock’s decaying uranium.
Radiation is so pervasive that geologists have uncovered evidence of 14 naturally occurring nuclear reactors. It’s coming out of the walls of the U.S. Capitol in Washington and New York’s Grand Central Terminal. Your cat is radioactive, your dog is radioactive, your friends and your family are all radioactive, and so, as it turns out, are you. Right now your body is giving off radiation and, every time you and another human being get together, you irradiate each other.
But there is, in all this, some good news.
The good news, though, is in that word: overdose. We’re not dropping dead from radiation poisoning on a daily basis because, like all poisons, it isn’t the particular atom that will get you. It’s the dose. And damage from radioactivity requires a much greater dose than any of us would have believed.
Our current knowledge comes from two decades long studies. The United Nations spent 25 years investigating the Chernobyl disaster Besides the U.N.’s Chernobyl report and the most extensive data on human exposure to radiation is the American-Japanese joint study of hibakusha—”explosion-affected persons”—the 200,000 survivors of Hiroshima and Nagasaki. Also expect more information to come from the data gathered from the Fukushima nuclear crisis.
Information comes from Craig Nelson’s book, “The Age of Radiance: The Epic Rise and Dramatic Fall of the Atomic Era,” published by Scribner.
Measuring background radiation
To do this we connected our brand new Geiger-Muller tube to our brand new counter.
The counter must always be zeroed before any radioactivity experiment is begun. When we were ready (Year 13) we switched on the counter and a stop clock and measured the number of counts recorded in a 5 minute period. No other radioactive sources that could affect the result were in the vicinity of the experiment. We took several measurements and found the average counts in 5 minutes. We then divided the average count by 300 seconds (the number of seconds in 5 minutes) and obtained a value of 11 counts per second or 11 Bq.
The becquerel (symbol Bq) is the SI derived unit of radioactivity. One Bq is defined as the activity of a quantity of radioactive material in which one nucleus decays per second. It is named after Henri Becquerel, who shared a Nobel Prize with Pierre and Marie Curie in 1903 for their work in discovering radioactivity.
The effective dose of all kinds of radiation is measured in a unit called the Sievert, although most doses experienced are much lower than a Sievert, so figures are given in millisieverts (mSv), which are one-thousandth of a Sievert.
The sievert is named after Rolf Maximilian Sievert, a Swedish medical physicist.
Having read that potatoes, carrots, brazil nuts and bananas can give off radioactivity we decided that we needed to measure it. Mrs Ul-Haq donated a banana, Ms Lane donated a carrot and a potato, Ms Rahman donated a carrot and Ms Harrison donated some brazil nuts. Disappointingly none of them gave values higher than the background count but we suspect that you need a more sensitive detector than a school G-M tube,
We also measured the radioactivity from dust we had collected from home and I am sure our parents will be relieved that we only got a background count value for this too.
Identifying alpha, beta and gamma radiation
From work we did during our GCSE science we already knew that there are three types of radioactivity, alpha, beta and gamma and from our work on particle physics we had some idea of how they come about.
Investigating Alpha radiation
Alpha particles consist of two protons and two neutrons bound together into a particle identical to a helium nucleus. They are generally produced in the process of alpha decay of heavier (106 u atomic mass or higher) atoms. The nuclei of these atoms are very “neutron rich” (i.e. have a lot more neutrons in their nucleus than they do protons) which makes emission of the alpha particle possible. The fundamental interactions responsible for alpha decay are a balance between the electromagnetic force and nuclear force. Alpha decay results from the Coulomb repulsion between the alpha particle and the rest of the nucleus, which both have a positive electric charge, but which is kept in check by the nuclear force.
After an atom ejects an alpha particle, a new parent atom is formed which has two less neutrons and two less protons. Thus, when uranium-238 (which has an atomic number, Z of 92) decays by alpha emission, thorium-234 is created (which has a Z of 90).
Because alpha particles contain two protons, they have a positive charge of two. Further, alpha particles are very heavy and very energetic compared to other common types of radiation. These characteristics allow alpha particles to interact readily with materials they encounter, including air, causing many ionizations in a very short distance. Typical alpha particles will travel no more than a few centimetres in air and are stopped by a sheet of paper.
Of course, as we are now in year 13, we can investigate this ourselves.
Alpha Particle Detector/Spark Counter
The above apparatus is a highly visible instrument for showing the random nature of radiation. It produces very bright sparks when alpha particles are ionised on the circular wire grid. It comes complete with sliding holder for the radiation source and an accurate scale to measure the effects of distance between the source and the grid. You can attach a counter to it to count the ionisation activity but ours was being used in another experiment.
When setting up the spark counter you use the highest potential difference that does not result in any sparks. This means that when the source is placed in the little holder any sparks are produced by the alpha source.
Alpha radiation, having a 2+charge, is the most highly ionising of all the types of radioactivity. The particles therefore are easily absorbed and don’t travel very far.
(not us unfortunately. Perhaps Mrs Hare will video next year’s year 13)
As alpha radiation doesn’t travel far so Matthew and Wing Chung don’t have to worry about being too near the source. They found that sparks stopped when the source was moved an average distance of 2.4 cm from the wire grid. So 2.4 cm is the range of the alpha source in air. Our alpha source is Americium-241 (2μCi – 74kBq) with a half life of 433 years.
In the picture below Matthew and Wing Chung are showing that paper can stop alpha radiation as with the paper between the source and the wire grid no sparks occurred.
We then repeated the experiment using a GM tube and counter. Remembering to take a background count first.
The Geiger–Müller tube (or G-M tube) is the sensing element of the Geiger counter instrument used for the detection of ionizing radiation. It was named after Hans Geiger who invented the principle in 1908,and Walther Müller who collaborated with Geiger in developing the technique further in 1928 to produce a practical tube that could detect a number of different radiation types.
The tube consists of a chamber filled with a low-pressure (~0.1 atm) inert gas. This contains two electrodes, between which there is a potential difference of several hundred volts. The walls of the tube are either metal or have their inside surface coated with a conductor to form the cathode, while the anode is a wire in the centre of the chamber. When ionizing radiation strikes the tube, some molecules of the fill gas are ionized, either directly by the incident radiation or indirectly by means of secondary electrons produced in the walls of the tube. This creates positively charged ions and electrons, known as ion pairs, in the gas. The strong electric field created by the tube’s electrodes accelerates the positive ions towards the cathode and the electrons towards the anode. Close to the anode in the “avalanche region” the electrons gain sufficient energy to ionize additional gas molecules and create a large number of electron avalanches which spread along the anode and effectively throughout the avalanche region. This is the “gas multiplication” effect which gives the tube its key characteristic of being able to produce a significant output pulse from a single ionising event.
For alpha, low energy beta and low energy g-ray detection the usual form of the GM-tube includes is a cylindrical end-window tube. This type has a window at one end covered in a thin material through which low-penetration radiation can easily pass. Mica is a commonly used material due to its low mass per unit area. The other end houses the electrical connection to the anode. The end window tube type is used for low penetration particle radiation.
The efficiency of detection of a G-M tube varies with the type of incident radiation. Tubes with thin end windows have very high efficiencies (can be nearly 100%) for high energy beta, though this drops off as the beta energy decreases due to absorption by the window material. Alpha particles are also absorbed by the window. As alpha particles have a maximum range of less than 50 mm in air we had to put the source right next to the mica window to detect the radiation. We were able to move the source a little way from the window (a couple of mm) to slip some paper in the gap, resulting in a count rate equal to the background radiation. In this experiment we measured the counts over one minute and divided this number by 60 to get counts per second. The results of this experiment was in good agreement with the spark counter in that alpha radiation is stopped by paper and a few centimetres of air.
The counting efficiency of photon radiation (gamma and X-rays above 25 keV) depends on the efficiency of radiation interaction in the tube wall, which increases with the atomic number of the wall material. Chromium iron is a commonly used material, which gives an efficiency of about 1% over a wide range of energies.
Investigating Beta radiation
Our beta source is R.A.SOURCE STRONTIUM 90
5µCi (185 kBq) of Strontium90 in equilibrium with its daughter nuclide Yttrium90, incorporated in a silver disc allowing the major proportion of the Beta radiation to emerge.
Beta minus decay is a radioactive process in which an electron is emitted from the nucleus of a radioactive atom, along with an unusual particle called an antineutrino. The neutrino is an almost massless particle that carries away some of the energy from the decay process. Because this electron is from the nucleus of the atom, it is called a beta particle to distinguish it from the electrons which orbit the atom.
Like alpha decay, beta decay occurs in isotopes which are “neutron rich” (i.e. have a lot more neutrons in their nucleus than they do protons). Atoms which undergo beta decay are located below the line of stable elements on the chart of the nuclides, and are typically produced in nuclear reactors. When a nucleus ejects a beta particle, one of the neutrons in the nucleus is transformed into a proton. Since the number of protons in the nucleus has changed, a new daughter atom is formed which has one less neutron but one more proton than the parent. For example, when rhenium-187 decays (which has a Z of 75) by beta decay, osmium-187 is created (which has a Z of 76). Beta particles have a single negative charge and weigh only a small fraction of a neutron or proton. As a result, beta particles interact less readily with material than alpha particles.
is another example of beta minus decay
This process is helped by the weak interaction. The neutron turns into a proton through the emission of a virtual W− boson. At the quark level, W− emission turns a down-type quark into an up-type quark, turning a neutron (one up quark and two down quarks) into a proton (two up quarks and one down quark). The virtual W− boson then decays into an electron and an antineutrino.
From our GCSE work we already knew that beta radiation can be stopped by aluminium but at A level we need to know more than this. Questions we needed to answer were how does the activity of beta radiation change with distance in air and how does the thickness of the aluminium absorber affect the quantity of beta radiation detected.
Of course the first thing we needed to do before any of the beta experiments was to find an average background count which needed to be subtracted from all the other beta readings.
The above picture shows Pameer carrying out the experiment that investigated how the distance between the beta source and the GM tube affected the activity detected. Notice that none of us ever stand in front of or behind the sources.
The aim of the experiment was to see what happens to the intensity of the radiation source with increasing the distance between the source and the detector. The prediction of the experiment was that the intensity of the source should decrease with distance from the source.
At the start of the experiment the apparatus was set up with the beta source as close to the GM tube as possible. The counts were recorded after sixty seconds to enable the counts per second to be calculated. This was then repeated for each distance between the GM tube and the source.
After taking readings of count rate from Geiger counter and the distance. Then finding the correct count rate, meaning subtracting the background radiation from all count rate readings, below is the graph of correct count rate against distance.
The graph supported our prediction. In the experiment absorption of the beta radiation and the fact that it spreads out are the reasons why the intensity decreases with distance.
The shape of the graph does indicate that the relationship between count rate and distance could be exponential or that the count rate obeys the inverse square law.
A quick look at the graph showed that the relationship wasn’t exponential because each time the distance value was increased by 1 the count rate did not decrease to one half of its previous value. If we had used a smaller distance between source and GM tube and used smaller increments of distance we may have seen an exponential relationship.
We then looked at whether the relationship obeyed the inverse square law, i.e. as the distance increases by a factor by 2 the count rate should drop by a factor of 4. The best way to visualise this is to plot a graph of count rate against 1/(distance)^2. Radiation does spread out radially and does covers a bigger and bigger area as you move away from the source so beta radiation could be proportional to d^2, so its intensity could decrease as 1/d^2 decrease.
However, by looking at my graph we can say that Beta radiation (source) does not obey the inverse square law.
The reason why the inverse square law is not obeyed for beta radiation is that electrons are loosing energy continuously, so after a specific distance, there is no radiation. Also the the length of the GM tube should really be factored in.
The picture below show Matthew investigating how beta radiation is absorbed by various materials.
As always we recorded an average background count before using the beta source.
Just out of interest we did check to see if paper had any affect on the count rate when it was placed between the GM tube and source. It didn’t.
The apparatus was set up as shown in the diagram. The GM tube was placed at a constant 10cm from the source holder.
As mentioned before and in all the experiments that used the cap sources a pair of long-handled forceps was used to place the source in the holder. The counts were recorded for sixty seconds each time to obtain the counts per second and the first count rate recorded was for no absorber present (I0).
A micrometer screw gauge was used to record the thicknesses (x) of each of the aluminium absorbers and the corrected count rates (I) were recorded.
Firstly we plotted a graph of corrected count rate against aluminium thickness to see what the graph looked like.
The graph does look like there could be an exponential relationship so the next stage was to plot a graph of lnI against absorber thickness (x) for the aluminium absorbers.
We were quite pleasantly surprised to see that there did appear to be an exponential relationship. The gradient of the graph is called the absorption coefficient (μ) for aluminium. The equation is
where I equals the count rate, I0 equals the count rate and x is the thickness of the absorber.
Of course we might have found that using a greater thickness of absorbers may have produced something similar to beta radiation in air results.
Investigating gamma radiation
R.A.SOURCE COBALT 60
5µCi (185 kBq) of Cobalt60 and is covered by an aluminium disc to shield beta particles so that only gamma radiation is emitted (but we still kept the cap on the GM tube just in case).
Gamma radiation, also known as gamma rays, and denoted by the Greek letter g, refers to electromagnetic radiation of extremely high frequency and therefore high energy per photon. Gamma rays are ionizing radiation, and are thus biologically hazardous. They are classically produced by the decay from high energy states of atomic nuclei (gamma decay), but are also created by other processes. Paul Villard, a French chemist and physicist, discovered gamma radiation in 1900, while studying radiation emitted from radium. Villard’s radiation was named “gamma rays” by Ernest Rutherford in 1903.
The emission of gamma rays requires only 10^-’12 seconds, meaning it occurs instantaneously. Since gamma rays are neutral and massless, there is no change in atomic number as well as mass number in daughter nuclei compare to parent nuclei in gamma decay. That is the reason, gamma emission is also known as isotopic transition which involves intermediate metastable excited states of the nuclei.
When the energy of gamma rays transfer to one of the most tightly bound electrons, that electron can be ejected from the atom and results photoelectric effect. The best example of gamma emission is beta decay of cobalt-60 forms Nickel-60 with the emission of gamma rays involve two nuclear reactions.
We should point point out that Mev is an alternative energy unit to the joule. It is used for tiny quantities of energy.
As with the beta experiment we carried out two separate experiments. One to investigate how the gamma activity changes with distance between the GM tube and the source and how the activity changes with absorber thickness.
As always we found an average count rate first which we then subtracted from any subsequent measurements.
The graph doesn’t look exponential but as gamma is an electromagnetic wave it should obey the inverse square law.
In physics, an inverse-square law is any physical law stating that a specified physical quantity or intensity is inversely proportional to the square of the distance from the source of that physical quantity. In equation form:
The lines represent the flux emanating from the source. The total number of flux lines depends on the strength of the source and is constant with increasing distance. A greater density of flux lines (lines per unit area) means a stronger field. The density of flux lines is inversely proportional to the square of the distance from the source because the surface area of a sphere increases with the square of the radius. Thus the strength of the field is inversely proportional to the square of the distance from the source.
The counts per minute of the gamma radiation represents its intensity so the if gamma radiation obeys the inverse square law then doubling the distance between source and GM tube should cause the counts per minute of the gamma radiation drop by 4.
Well the graph doesn’t seem to show the inverse square law, but if we were to ignore the two furthest points which correspond to the two shortest distances between the source and GM-tube we could argue that there is a linear relationship.
The main problem with these type of experiments, especially with gamma, is that we really should have allowed for the length of the tube. To reduce this error we could have used the side of the GM tube rather than the mica window side. Another large cause of uncertainty is the variation of the count rate due to the random nature of decay. If we had had more time we should have repeated each reading several times and used the average in our graphs. We could also argue that the little radiation cap used in our experiments is not a point source.
The above graph shows what the inverse-square law relationship should have been for gamma radiation. #3 and #4 refer to two different cobalt sources (4 is more energetic than 3). The person who got these results used much smaller distances between source and detector than we did.
The next experiment involved seeing how absorbers affected the count rate and was designed to allow us to understand the absorption and range of gamma radiation through lead.
Firstly we set up the GM tube and did a reading for the background radiation over two minutes with the source holder in place. This would give a constant gap between source and GM tube of 10cm. The background count was repeated several times to obtain and average. This value was subtracted from each absorber reading.
Just out of interest we tried putting a sheet of aluminium and a sheet of paper (separately) in the gap to see if they would have any affect on the gamma count rate. They didn’t so our GCSE science teachers can now breathe a sigh of relief.
We used a micrometer to measure the thickness of the lead sheets used in the experiments. Each time a different lead absorber thickness was placed in the gap we recorded the counts for 2 minutes and noted them down.
The above picture shows Aslam and Matthew getting the first absorber in place.
Aslam and Matthew just waiting for the two minutes to end so that they can record the counts from the gamma source for the radiation that could get through the lead sheet.
We wanted to see if gamma radiation had the same relationship with lead thickness as aluminium did with beta radiation. The equation is
where I equals the count rate, I0 equals the count rate and x is the thickness of the absorber.
If the relationship is the same a graph of ln I against x should be a straight line with a gradient equal to m (the absorption coefficient for lead).
The graph below is a bit bumpy but we can argue that the line of best fit shows there is an exponential relationship between thickness of the lead and the counts recorded in 2 minutes.
Now if you are a physics teacher reading this you might be asking why we haven’t done error analysis on any of the experiments. The answer is that we didn’t have very much time as we only had one session to do all the experiments and Mrs Hare wanted us to do error analysis on the half-life experiment. I am sure she will torture next years year 13 with it.
In reality lead cannot stop gamma radiation completely so the term half-thickness of lead is used. In other words what thickness of lead has to be used to reduce the corrected count rate by a half.
Another method of identifying alpha, beta and gamma radiation is to place the radioactive emissions in the path of a magnetic field.
Moving charged particles experience a force when they travel in a magnetic field that is at right angles to their path. The force acts mutually at right angles to the direction the particle is travelling and the direction of the field so it takes a circular path.
Gamma rays are not charged so they won’t be deflected by a magnetic field.
The direction it will go in can be found using Flemings left hand rule. At GCSE we did not need to know which way it will move but at A level we do.
Just as an interesting aside we noticed that TAP physics had an interesting experiment on the absorption of radiation by biological materials
So as we had some spare potatoes we decided to investigate how good the potatoes were at absorbing radiation. The practical does say you should use a beta source but that was being used elsewhere so we decided to give the gamma source a go. Another problem was that the GM tube was also being used but we did have a spare piece of equipment that contained the detector and counter.
The picture below shows Alfie preparing his samples of carrots and potatoes although he only had time to use the potatoes. He used a vernier calliper to measure the thickness of each piece of potato. He did dispose of the vegetables after the experiment as the donors didn’t want them back. He did think about making an Irish stew with them but a) he didn’t have any meat, b) the vegetables didn’t look very nice c) there are no cooking facilities in the lab and most importantly d) as we were working with radioactive sources we shouldn’t have any food (as food) in the lab.
Experiment to discover the relationship between the thickness of potatoes and gamma radiation by Alfie Mussett
The experiment I performed was to discover how good potato is absorbing gamma radiation. I first did a measurement of the back ground count using the ratemeter and then, after I cut up the a potato into varying thicknesses, I placed the potato slices between the gamma source and the ratemeter.
For each thickness of potato, I used the ratemeter to measure the counts over the course of two minutes. The counts recorded was due to the gamma radiation getting through the potato slices and reaching the ratemeter.
The graph below looks like it could be exponential.
The graph below shows the relationship is exponential.
Mrs Hare was very surprised by this result. She didn’t think that the potato would have any effect on the counts recorded. But the graphs show that not only does the potato absorb gamma but that there is an exponential relationship.
In reality I think the relationship is more to do with the source (cobalt) also emitting some alpha radiation (even though I thought we had shielded his). It is the alpha radiation that is being stopped by the potato resulting a lower radiation count because the Geiger counter can’t distinguish between types of radiation and gamma radiation being stopped by a potato doesn’t make any sense.
I don’t think we will be marketing potato as a credible shield against gamma radiation.
So our GCSE teachers were correct. Alpha radiation is stopped by a few centimetres of air or a single sheet of thin paper. Beta radiation is stopped by several cm of aluminium and gamma radiation is greatly reduced by several cm of lead (an several metres of concrete but we didn’t test this).
One thing that did worry us a little was that alpha, having the greatest charge, would be expected to give the highest count rate as it is highly ionising and gamma having the lowest because it isn’t charged. This wasn’t the case. We think the reason why gamma radiation appeared to have such a high count rate was because being uncharged it didn’t lose much energy interacting with matter on its way to the GM tube. Gamma-rays are referred to as indirectly ionising radiation since, having no charge, they do not directly apply impulses to orbital electrons as do alpha and beta particles. Gamma rays proceed through matter until there is a chance of interaction with a particle. If the particle is an electron, it may receive enough energy to be ionised, where it causes further ionisation by direct interactions with other electrons. As a result, gamma rays can cause the liberation of directly ionising particles (electrons) deep inside a medium. Because these neutral radiations undergo only chance encounters with matter, they do not have finite ranges, but rather are decreased in an exponential manner. In other words, a given gamma ray has a definite probability of passing through any medium of any depth releasing some electrons as it travels and it is these electrons that cause further ionisation.
Measuring the half life
Half-life (t½) is the amount of time required for a quantity to fall to half its value as measured at the beginning of the time period. While the term “half-life” can be used to describe any quantity which follows an exponential decay, it is most often used within the context of nuclear physics and nuclear chemistry, that is, the time required, probabilistically, for half of the unstable, radioactive atoms in a sample to undergo radioactive decay.
The original term, dating to Ernest Rutherford’s discovery of the principle in 1907, was “half-life period”, which was shortened to “half-life” in the early 1950s. Rutherford applied the principle of a radioactive elements’ half-life to studies of age determination of rocks by measuring the decay period of radium to lead-206.
Half-life is used to describe a quantity undergoing exponential decay, and is constant over the lifetime of the decaying quantity. It is a characteristic unit for the exponential decay equation.
Because we really need to repeat half-life experiments in A-level physics we usually define half-life as the average time taken for the activity or the number of radioactive particles to halve.
As a preparation for investigating the half life of protactinium we modelled the decay using skittles. The advantage of this experiment is that we get to eat the “decayed” skittles.
The experiment was quite simple. Firstly we checked that all the skittles had an S on one side (we ate the ones that didn’t). We then counted the remaining skittles (this is tip 0) and put them into a plastic cup. We shook the skittles gently and dropped them on to the paper covered bench. We ate the ones that had the S face upwards, counted the remaining ones and put them back into the cup (tip 1). We shook the skittles in the cup again, tipped them onto the paper, ate the ones with the S face upwards, counted the remaining and put them back into the cup (tip 2). We continued with this until there were no more skittles.
Clockwise from left shows Alfie, Aslam, Matthew and Pameer counting skittles.
The above graph can be used directly to find the half life. Using the graph you can see the number of tips needed to halve 750 skittles to 375 was about 2. To halve again to 187.5 required another 2 tips and to halve again to about 93.8 required another 2 tips. Unfortunately the model breaks down when the skittle numbers gets too small.
Now the graph does look like it could be exponential. To see if it was we need to plot a graph of ln (number of skittles remaining) against number of tips.
We could argue that the graph does begin with a straight part so when there was a large quantity of skittles there was an exponential relationship between the number of tips and the number of skittles of remaining.
Unfortunately we couldn’t repeat our readings as we had eaten the skittles.
Radioactive decay, also known as nuclear decay or radioactivity, is the process by which a nucleus of an unstable atom loses energy by emitting particles of ionizing radiation. A material that spontaneously emits this kind of radiation, which includes the emission of energetic alpha particles, beta particles, and gamma rays, is considered radioactive.
Radioactive decay is a completely random process at the level of single atoms, in that, according to quantum theory, it is impossible to predict when a particular atom will decay. However, the chance that a given atom will decay is constant over time. For a large number of atoms, the decay rate for the collection can be calculated from the measured decay constants of the nuclides (or equivalently from the half-lives).
Radioactivity is one very frequent example of exponential decay. The law describes the statistical behaviour of a large number of nuclides, rather than individual ones (the relationship breaks down for small quantities). In the following form the number of nuclides or nuclide population N, is a discrete variable (a natural number), but for any physical sample N is so large (amounts of L = 10^23, Avogadro’s constant) that it can be treated as a continuous variable. Differential calculus is needed to set up differential equations for modelling the behaviour of the nuclear decay.
Consider the case of a nuclide A decaying into another B by some process A → B (emission of other particles, like electron neutrinos νe and electrons e– in beta decay, are irrelevant in what follows). The decay of an unstable nucleus is entirely random and it is impossible to predict when a particular atom will decay. However, it is equally likely to decay at any time. Therefore, given a sample of a particular radioisotope, the number of decay events −dN expected to occur in a small interval of time dt is proportional to the number of atoms present N, that is
Particular radionuclides decay at different rates, so each has its own decay constant l
The negative sign indicates that N decreases as time increases, as the decay events follow one after another. The solution to this first-order differential equation is the function:
Where N is the number of undecayed particles at time t, N0 is the original number of undecayed particles, γ is the decay constant for that reaction and t is the time when N (t) is measured.
The equation can also be written in terms of the activity, A (counts per second), of the sample
During GCSE we only have to plot a graph of count rate against time and use the graph to see what time is needed for the count rate to halve. At A level we have to be more mathematical.
We can re-write the above formula as
We can then plot a graph of ln A against t and the gradient will equal the decay constant l.
Once we know l we can calculate the half life t½
In school we use a protactinium generator to allow us to investigate how protactinium decays with time.
The isotope of protactinium 234Pa has a half-life of several tens of seconds. You can monitor its decay using a GM tube connected to a counter. It would be easier to use a data logging interface and computer to determine its half-life directly but at the moment we don’t have the necessary equipment. It is on Mrs Hare’s shopping list.
The 238U is in the form of uranyl nitrate dissolved in water and is contained in a sealed plastic bottle. The bottle also contains an oily solvent that floats above the water. This sealed unit can only be purchased like this and our wonderful technicians will check our bottle regularly to see it isn’t leaking. The bottle must never be opened.
The sample of 234Pa is produced by the decay of 238U. Pa234 is the grand-daughter of U238: alpha decay to Th234 followed by beta decay to Pa234.
When the bottle is shaken some of the 234Pa in the watery layer dissolves into the oily layer. Once the two layers have separated out, no more 234Pa moves into the oily layer, so we have a fixed sample of 234Pa in the oily layer. 234Pa emits energetic beta radiation, which can penetrate the plastic bottle and travel some distance in air. This is the radiation that we monitored.
Without shaking the bottle, the apparatus was set up as in the picture below.
We measured the background radiation (it came from the bottle and the lab), counting for fine minutes. We did this several times, found and average and divided the average by 300 seconds to get the average background count per second.
We shook the bottle for about 30 s and placed it back in position. We waited for the layers to settle and started the clock. The GM tube window was as close to the oily layer as possible.
Aslam and Wing Chung waiting patiently to start the experiment with stop watch, paper and pen at the ready.
The experiment wasn’t difficult but it did need a lot of concentration. The stop watch and the counter were switched on at the same time and the idea was to record counts for 10 seconds every 30 seconds making sure that the counter was zeroed after each 10 second count.
Aslam and Wing Chung getting ready to take down the first 10 second count.
And here it is.
When we were setting out our table of results we did subtract the background count to obtain the corrected count per 10 seconds. We then divided each number by 10 to get the corrected count rate per second which we could give the unit Bq (becquerel) to.
For interest we did plot a graph of corrected count rate against time to see what it looked like.
Graph looks like it could be exponential. We made the right decision to stop at 5 minutes as the relationship breaks down when the quantity of radioactive atoms becomes too small.
This graph shows that the relationship is most definitely exponential. The gradient equals the decay constant, l,
This value is in good agreement with the actual value of half-life of about 72 seconds.
We were slightly surprised that the results were so good because when we were measuring the counts over 10 seconds the protactimium would not have a constant count rate as it would be still be decaying. This is why data-logging would be better as we have would have been able to measure a count over a much tinier time interval.
Details of the decay:
234Pa is extracted from a solution containing the parent 234Th and ’grandparent’ 238U with which it is in equilibrium. Once extracted the decay of 234Pa was recorded. About 95% of the protactinium is removed together with some uranium when the bottle is shaken. The GM tube does not detect the alpha from the 238U or the weak beta particles (about 0.2 MeV) from the 234Th but detects only the energetic (2.32 MeV) beta radiation from the 234Pa.