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Radioactivity and nuclear decay: presentation script Pratap Singh, The Perse School 09/09/14 Slide: Title Over the last year, I have been reading about and studying the different types of radiation and how they are detected, especially in the context of cosmic rays. This talk is about radioactivity. ! Slide: Overview Specifically: I will begin by giving a simple qualitative description of some core physics “laws” or “principles”. Then, based on these, I will describe the processes that lead to the various types of radiation, and how and why they interact with matter as we observed on Friday. I will describe a very simple device that can detect ionizing radiation - the Geiger-Müller tube that we used on Friday. Finally, I will go over some examples of radioactivity - the decay chain of uranium-238, the chain-reaction fission of uranium-235, and the concept of critical mass (may be skipped). In case I don’t give exactly correct explanations because I don’t know something very well, please jump in and correct me. ! Slide: Photoelectric effect Let’s start with the physics principles. One of the most fundamental principles of physics is the conservation of energy. We know that a positively charged particle, like a nucleus, and a negatively charged particle, like an electron, will attract each other. So if we pull an electron away from the nucleus, it must have more energy. And when an electron falls back closer to the nucleus, it must lose this excess energy in some way. The energy that is released takes the form of a photon - a particle with no mass and pure energy. This is the photoelectric effect. The reverse process can also take place - when a photon strikes an electron, it may be absorbed and cause the electron to jump to a higher-energy state. More generally, whenever an atom is in any kind of excited state, if it returns to a lower-energy state the excess energy will be radiated off as a photon. This becomes important later in the discussion of gamma rays, but we can also apply it to other interesting observations. For example: Due to some other principles which we don’t need to go into, electrons can only exist at certain quantized energy states around the nucleus. So for a photon to be absorbed, its energy must be greater than or equal to the energy required by the electron to jump to the next allowed energy state. Now we can see why glass is transparent to visible light - photons of visible light do not have enough energy to move any electron in the glass to its next energy level, so all the photons can do is pass straight through the glass. On the other hand, no electrical conductor will be transparent - the delocalized electrons in the metal can be excited by very small amounts of energy, so virtually no photons will be able to pass through without exciting an electron. The full theoretical explanation of the photoelectric effect was given by Albert Einstein in 1905, and won him a Nobel Prize. ! Slide: Mass-energy equivalence The next principle is one of the best-known equations in physics, and was again given by Einstein - E = mc^2. This equation states that mass and energy are actually two sides of the same coin - if a particle gains some energy, its mass increases. We will need this when looking at the energy released in the fission examples. ! Slide: Fundamental forces Now we come to the main principles involved in radioactivity. Up until the start of the 20th century, all observations in physics, chemistry, etc could be explained by just two fundamental forces - gravity and electromagnetism. But when we found out what the inside of an atom looks like, a problem arose. The nucleus of an atom contains many positively charged protons, which all repel each other due to the electromagnetic force. However, nuclei do not spontaneously disintegrate and fly apart. So the question is: what holds the nucleus together? One idea is gravity - but gravity is just too weak. It is actually 10^37 times weaker than the electromagnetic repulsion between the protons. Slide: Strong force The question was eventually answered by a chain of discoveries that led to the postulation of another fundamental force, called the strong force. Nucleons (ie protons and neutrons) are each made up of three smaller particles called quarks, and the strong force is what holds these quarks together to form a nucleon. The strong force is, unsurprisingly, very strong: it binds quarks together with so much force that they gain a very high potential energy. From the mass-energy equivalence, this means that nucleons have a mass roughly 100 times greater than the sum of the masses of the three component quarks. ! Slide: Residual strong force However, the mathematics of the strong force predicts that the effect of this attraction goes beyond the boundaries of the nucleon: a small residual force, called the residual strong force or the nuclear force, acts for a very short distance outside the nucleon. The residual strong force has a very strange behavior: when nucleons are less than 0.7 femtometers (that is, 0.7 x 10^-15 meters) apart, the force repels them apart. But at 0.7 femtometers it becomes an attraction, and reaches the maximum attraction at 0.9 femtometers. It then exponentially decreases to negligible strength beyond about 2.0 femtometers. The effect of this residual strong force is to bind neighboring nucleons together, and overcome the electromagnetic repulsion between protons. This is the force that holds the nucleus together. Slide: Why neutrons? The residual strong force provides the answer to another question: why are there neutrons? It turns out that if there are only protons in the nucleus, they would be too close together and the electromagnetic force would rip them apart. Neutrons effectively separate out the protons in the nucleus, and provide more attraction via the residual strong force; they reach a point where the residual strong force overcomes the electromagnetic repulsion and holds the nucleus together. ! ! Slide: How many neutrons? From this reasoning, we can see that if there are vastly too many protons relative to the number of neutrons in a nucleus - for example, oxygen-12, with 8 protons but only 4 neutrons - a proton will just be ejected from the nucleus, leaving us with nitrogen-11. This again turns out to have too many protons, and will eject a proton to leave carbon-10. Carbon-10 is still unstable but closer to stability, so here something different happens - we’ll come back to it. On the other hand, if there are vastly too many neutrons, it turns out that neutrons will also be ejected to reach a more stable state - for example, oxygen-25, with 8 protons and 17 neutrons, will eject a neutron to leave oxygen-24. ! Slide: Weak force Nuclei such as carbon-10 and oxygen-24 are unbalanced, but not so heavily that they will eject protons and neutrons. They decay in a different way, and to understand this, we actually need to introduce the fourth and final fundamental force, known as the weak force. I don’t know what the underlying mechanism of the weak force is, but it has a simple high-level effect - if there are too many neutrons, it causes some neutrons to decay into protons; and if there are too many protons, some decay into neutrons. This allows the nucleus to move towards a more stable state, with the right ratio of protons to neutrons. For example, four neutrons in the oxygen-24 from earlier will decay in this way into protons, turning into magnesium-24 (a stable isotope with 12 protons and 12 neutrons). On the other hand, one proton in carbon-10 will decay into a neutron, leaving stable boron-10. Slide: Weak force: details However, there is a problem with this explanation - if we start with a neutron, with no charge, how can we be left with a positively charged proton? In the actual mechanism, which is called beta decay, an electron and a very small neutral particle called a neutrino are also ejected. We want to be able to represent this compactly, so we write a sort of equation similar to a chemical symbol equation. So the equation for a neutron’s beta decay, called beta-minus decay, is as follows: n —> p + e^- + v^-_e where n is a neutron, p is a proton, e^- is an electron, and v^-_e is an antineutrino. Similarly, a proton decays into a neutron as follows via beta-plus decay: p —> n + e^+ + v_e This time, we get e^+, which is the anti-particle of an electron, called a positron. The neutrino is a regular neutrino. Slide: Beta decay The positron, as it flies through normal matter, could interact with a normal electron. They would annihilate each other and release the energy as two high-energy gamma rays; so this type of decay could lead to gamma radiation. In both cases, the electron is radiated off with very high energy, and so is detected as beta radiation. So this process is the origin of the beta radiation we observed on Friday. ! Slide: Summarizing forces Let’s pause and summarize the roles of the four fundamental forces in the nucleus. Gravity - irrelevant. It is too weak to play a role in normal matter. Electromagnetism - behaves the same as on a macroscopic scale. Causes protons to repel each other, according to an inverse-square law. The residual strong force - behaves in a very peculiar way. Holds nucleons at a very precise distance from each other, and binds the nucleus together - balancing electromagnetic repulsion. No effect outside of the nucleus. The weak force - allows protons and neutrons to change into one another releasing beta radiation, so that the nucleus moves closer to a stable ratio of protons to neutrons. ! ! ! Slide: alpha decay We’ve seen what happens when the ratio of protons to neutrons is unbalanced. However, this isn’t the only criterion for nuclear stability. In very large nuclei, the range of the residual strong force means that nucleons are attracted only to their nearest neighbors. But the protons are repelled by all of the other protons in the nucleus. This explains why larger nuclei need more neutrons than protons - they spread out the protons further and provide extra attraction via the residual strong force. Occasionally, a small part of the nucleus may be attracted so weakly that it randomly falls off. These chunks will move out of the range of the strong force and will then be accelerated off by the electromagnetic repulsion of the protons, leading to a new sort of radiation. It turns out that in almost all cases, only one particular type of chunk falls off - consisting of two protons and two neutrons. This is known as the alpha particle. Alpha particles are favored because they are very stable - the helium nucleus is actually the most stable nucleus of all. We can represent this in an equation as well. Let’s take the example of uranium-238, the most common type of uranium in nature. Since it has such a big nucleus, it decays via alpha decay. Losing two protons and two neutrons leaves an atom two places to the left in the periodic table - thorium-234. Summarizing: ^238_92 U —> ^234_90 Th + \alpha So alpha radiation arises when chunks of the nuclei of large atoms fall off. Slide: gamma decay When these two types of decay occur, a large amount of potential energy is converted into the kinetic energy of the resultant particles. This leaves these particles in higher-energy states. We know that due to the photoelectric effect, when the particles return to their lower-energy states, the excess energy will be radiated off as a photon. Typically, there is so much energy that the photon emitted is a high-energy gamma ray. This is the most common source of gamma radiation. The other source that I mentioned earlier is positron-electron annihilation. This covers the mechanisms of the three main types of nuclear decay, and the resulting radiation alpha, beta and gamma. ! Slide: Nuclide map Let’s see what sorts of nuclei are produced by these decay processes. ! ! ! ! Slide: zoomed-out nuclide map The diagram on the screen is known as a nuclide map. It shows all the different possible nuclei, with the number of neutrons increasing from left to right, and the number of protons increasing from bottom to top. ! ! ! Slide: zoomed-in nuclide map Each box represents a nuclide (a particular type of nucleus), and the colors represent how they decay. Black boxes are stable - they do not undergo any decay. All other nuclides want to decay into one of these black boxes. The map nicely illustrates the roles of the different types of decay. ! ! Slide: zoomed-out nuclide map (back one slide) Alpha decay is shown by a yellow box - this causes the nuclide to jump two boxes to the left and two down. We can see that this happens mostly with very large nuclei, as we predicted. Beta-minus decay (with a neutron turning into a proton) is shown in pink - this causes the nuclide to jump one box left and one box up, as it gains a proton and loses a neutron. We can see that this happens “below” the line of stable nuclei, where there are more neutrons than required. Beta-plus decay (with a proton turning into a neutron) is shown in light blue - this causes the nuclide to jump one box right and one box down. We can see that this happens “above” the line of stable nuclei, where there are more protons than required. Around the edges of the chart, we see other types of boxes. Those in orange have so many protons that they decay simply by ejecting one; they move one box down. Those in purple have the same problem but with neutrons they eject a neutron and move one box to the left. The last color on the diagram is green - representing a process called spontaneous fission. These nuclei are so big and unstable that they don’t just eject alpha particles they spontaneously smash into several large and small chunks. It is this process which can lead to a chain reaction, and this process which is used to generate nuclear power or build nuclear fission weapons. ! Slide: nuclide map zoomed with Am-241 in center On Friday, we used three radioactive sources, one for each type of radiation. The alpha source contained the radioactive isotope americium-241, represented by the yellow box in the center of the screen. Since this has a very large nucleus, it is unstable and decays via alpha decay, moving two boxes diagonally down and left in the nuclide map to neptunium-237. Slide: nuclide map zoomed with Sr-90 in center The beta source contained strontium-90, represented by the pink box in the center of the screen. Strontium-90 has more neutrons than it needs, so via beta-minus decay, one neutron decays into a proton emitting an electron. The nuclide moves one box diagonally up and left on the map, to give yttrium-90. ! ! ! Slide: nuclide map zoomed with Co-60 in center The gamma source contained cobalt-60, shown by the pink box in the center of the screen. The pink box tells us that cobalt-60 decays via beta-minus decay, going to nickel-60. However, the resulting nickel-60 nucleus is in an excited state; so via the photoelectric effect it releases its energy in the form of two photons. So much energy is released that the photons are actually emitted in the gamma-ray part of the electromagnetic spectrum. If you remember, the gamma source had a bigger container; this was to stop the beta particles emitted, so we only detect the gamma rays. Slide: Ionization We have seen how the various forces at work in the nucleus result in the three types of ionizing radiation. But the next question is: why is this radiation known as “ionizing”? How do alpha, beta, and gamma particles ionize matter? To understand this, we must divide the ionizing radiation into two types - charged and neutral. Alpha and beta particles are charged, and so will interact differently with matter than the uncharged gamma-ray photons. ! Slide: Ionization by charged particles An atom becomes ionized when an electron is knocked loose. When a charged particle moves past an atomic electron, their electric fields will interact. This results in some energy being transferred from the more energetic moving particle to the less energetic electron. When the charged particle has high energy, such as an alpha or beta particle resulting from nuclear decay, the energy transferred is often enough to rip the electron away from its nucleus. In this way, a charged particle can ionize an atom simply by passing by it. So alpha and beta radiation will ionize matter continuously along their path, and lose energy continuously in this way. A beta particle traveling at 96.7% the speed of light will ionize roughly 50 molecules per centimeter it travels through air. An alpha particle, with twice the charge, will interact even more strongly with matter and ionize many more molecules. The energy lost in these interactions is what leads to the short ranges of these particles, and is why they can be stopped by very small amounts of matter as we saw on Friday alpha particles are “stopped” by cigarette paper, beta particles by a thin sheet of aluminum. ! Slide: Ionization by uncharged gamma rays Uncharged gamma-ray photons behave very differently. Since they have no charge, they cannot interact with electrons at a distance - they must collide head-on with them. Since matter is mostly “nothing”, and only a tiny fraction of the space is “occupied” by electrons or the nucleus, the likelihood of a gamma ray striking a given electron is very small. So the gamma ray must pass through very many more atoms before it collides with an electron. A gamma-ray photon with the same energy as the beta particle from before (which ionized 50 air molecules per centimeter it traveled) would travel, on average, 170 meters before hitting an electron head-on and transferring all or part of its energy. This is why gamma rays are much more penetrating than alpha or beta particles. The gamma ray gives up its energy via the photoelectric effect. Usually, the electron is fully ejected from the atom without using up all of the gamma ray’s energy, in which case the gamma ray continues on as well at a lower energy; this type of interaction is known as a Compton scattering. As a result of this Compton scattering, a gamma ray can produce a beta particle and a less energetic gamma ray. Slide: The GM tube The common behavior of all these types of radiation is that they can ionize matter. We can use this to build a detector for ionizing radiation. There are many types of detectors, but the type we used on Friday is one of the simplest and most effective - the Geiger-Müller tube. The diagram on the screen shows a schematic of a GM tube. The tube consists of a sealed chamber, filled with a rarefied noble gas, and enclosed by a metal casing. There is a metal wire suspended in the chamber and insulated from the casing. The casing and the wire are then used as electrodes - they are connected to either end of a high-voltage power supply which maintains a potential difference of more than 500V between them. Since there is no conducting material, just a rarefied inert gas, between the electrodes, there is no complete circuit and current cannot flow. However, when an ionizing particle enters through the detector, it may ionize one of the atoms of gas. This will result in a positive ion and a free electron, which may attach to another neutral atom or remain free. In either case we get two oppositely charged particles inside the detector. These charged particles are influenced by the strong electric field, and each accelerate towards the oppositely-charged electrode. As they accelerate, they build up their own kinetic energy; so if they happen to hit another atom of gas, they will have enough energy to ionize it. This results in more ions being produced, which then accelerate and may produce more ions, etc. In this way a cascade proceeds, of positive particles towards the cathode and negative particles towards the anode. When they eventually hit the electrodes, a net transfer of charge takes place from the anode to the cathode, meaning that a small net current has flown around the circuit. This causes a brief pulse, which can be detected and amplified by other electronics. This pulse is the telltale signature of some kind of ionizing radiation passing through the detector. Slide: Example: decay chain of U-238 We have discussed how all of the three types of radiation arise from just a few underlying principles, and seen how they can ionize matter. Let’s use this knowledge to understand some well-known examples of radioactive decay. Uranium-238 is the most common isotope of uranium on Earth - it is a relatively common element with an abundance of roughly 1.8 parts per million in the Earth’s crust. This means there are probably at least a few grams of uranium, if not more, in the soil in the school grounds. Uranium-238 is a very long-lived isotope with a half-life of around 4.47 billion years. But it does decay, and we can understand its decay chain. Uranium-238 has a very large nucleus, so it will decay by alpha decay. This causes it to jump down to thorium-234. But this now has too many neutrons, so it undergoes betaminus decay twice to eventually reach uranium-234 again. … [equations on slide] … Finally, we get to lead-208, which has the largest stable nucleus of all known isotopes. Lead is a sort of boundary element, in that all elements with higher atomic numbers will eventually decay to either lead or elements lower than lead. Decay chains similar to this one are all present in the nuclide chart from earlier for all radioactive isotopes. ! ! Slides: Example: fission of U-235 Uranium-238 is the most common naturally occurring isotope of uranium, but it isn’t very commercially useful. A different isotope, uranium-235, is what is used in nuclear power plants. This isotope naturally undergoes alpha decay, but can be made to undergo nuclear fission and rapidly liberate large amounts of energy. Nuclear fission is a different reaction to the three types of decay, but it is governed by the same principles. The first step is to hit a uranium-235 nucleus with an energetic neutron. This results in a nucleus of uranium-236, but in a high-energy, unstable state. In fact, it is so unstable that it spontaneously breaks into two large fragments - nuclei of barium-141 and krypton-92. Crucially, these atomic masses don’t add up to 236 - three free neutrons are also ejected at high speeds. The fission process also releases some of the potential energy of the nucleus. We can summarize this process in an equation: n + ^235_92 U —> ^236_92 U* (* means excited) —> ^141_56 Ba + ^92_36 Kr + 3 n The three neutrons may go on to hit other uranium-235 nuclei, causing them to undergo fission in the same way. So a chain reaction can proceed. If it can be arranged that on average, even fractionally more than 1 of these neutrons goes on to cause another fission reaction, then a runaway chain reaction occurs: so much energy is released so quickly that a nuclear explosion takes place. However, if we can carefully control the number of neutrons that cause another fission to be exactly 1 out of the three, then a controlled chain reaction occurs, releasing energy at a constant rate. These sorts of arrangements are used in nuclear power plants. Slide: Thank you for listening Thank you for listening!