# RADIOACTIVE DECAY

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Physics (Notes on Chapters) Note on RADIOACTIVE DECAY, created by ibukunadeleye66 on 15/01/2014.
Note by ibukunadeleye66, updated more than 1 year ago
 Created by ibukunadeleye66 over 10 years ago
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Nuclear decay is- A process of disintegration that occurs when unstable nuclei decay in an attempt to attain stability, until their N/Z (neutron/proton) number falls within the stability limit/ band of stability. Disintegrates to a daughter nucleus that is more energetically stable.- Results in the emission of particles and EM radiation from an unstable nucleus.- A spontaneous process not affected by temperature or the environment- Random/unpredictable- Approximately follows an exponential decay process/ constant probability of decay per unit time/ activity or number of unstable nuclei in the sample reduces exponentially. (Any quantity that reduces to half its value in fixed intervals of time is an exponential process)Know the difference between random and spontaneous:Random: Unpredictable precise moment of disintegration, unpredictable emission of radiationSpontaneous: Process of radioactive decay cannot be sped up or slow down by physical or chemical means.Radioactive decay law: The number of radioactive nuclei will decrease in exponential fashion with time with the rate of decrease being controlled by the decay constant.(Comes from : the rate of decay/ activity is proportional to the number of nuclei)Decay constant : The probability of decay of a nucleus per unit time, and is characteristic of that particular nuclide. Units: time-1.Activity of a source:(Given initial activity and half-life, initial number of nuclei can be calculated from )Half-life: The time taken for half the nuclei in a given sample to decay.Method for measuring short half-life of an isotope: Place radioactive sample in a suitable container Using a GM tube, record the count rate A at equal intervals of time Plot a graph of lnA against time T. Find decay constant from the gradient of the line, and then determine half-life using equation . Method for measuring long half-life of an isotope: (For very long half-life, activity plot cannot be used as change in activity will be almost zero) Determine chemically the number of atoms N in the sample/isotope from the measured mass of the sample/isotope. Place radioactive sample in a suitable container Using a GM tube, record the count rate A at equal intervals of time Determine decay constant from formula , and then determine half-life using equation . Background radiation: Cosmic rays from outside the earth, decay of minerals present in materials/the earth.*Know how to measure background count, and find half-life in scenarios where there is background radiation.1. Identify if decay is to a stable value à Existence of background radiation2. Subtract initial by background rate3. Halve actual count rate4. Add actual count rate after half-life to background rate5. Read off time that gives (4)Explaining why activity of carbon from charcoal less than that of living wood: Amount of C-14 present determines the activity of the carbon. The charcoal or dead wood does not take in any more carbon dioxide and (hence) C-14, thus its activity is lower. Since C-14 is radioactive, the amount present in the charcoal decreases with time.Suggest why radioactive dating of carbon samples more than 20000 years old is unreliable: Too little radioactive carbon is left making detection of activity difficult to distinguish from background count.For long half-life activity can be said to be constant as during short time intervals, short compared to half-life of sample. Hence number of nuclei does not change significantly. Since activity proportional to the number of nuclei present, activity can be considered constant as well.A radioactive isotope has a half-life of five minutes. A particular nucleus of this isotope has not decayed within a time interval of five minutes. In the next five minute interval the nucleus has a 50% chance of decaying.When calculating power of emission of energy in a nuclear reaction, don’t forget to calculate the activity!!!Three types of Radioactive decay:- Alpha rays (helium nuclei)- Beta rays (electrons)- Gamma rays (EM radiation, photons)AlphaBetaGammaHigher probability of nuclear disintegration via alpha decay as alpha particle is quite stable. Occurs when nuclide has too many neutrons compared to protons.Beta minus decay usually occurs when nuclide has too many neutrons compared to protons. Beta positive decay usually occurs when nuclide has too many protons compared to neutrons, emitting a positron e+, the antiparticle to the electron (same mass but opposite charge).Neutrino: Emitted electrons were observed to have less energy, thus in order for linear and angular momentum to be conserved, theorized new particle neutrino. Zero charge and a very small rest mass.Emitted when a nucleus decays from an excited state to a lower state. Often follows an alpha or beta decay when resulting nucleus not in its lowest energy state. Alpha particle: Has discrete energies.Only two products in alpha decay: alpha particle and daughter nuclei. Daughter nuclei has discrete energy values; discrete velocities. Following conservation of momentum, alpha particle emitted in opposite direction of daughter nuclei with discrete velocities and thus discrete energies.Beta particle: Has continuous energy spectra, implying that energy not conserved in beta decay. Hence neutrino postulated to account for missing energy.Since three products formed, three particles can undertake an infinite number of directions and velocities. Hence beta particle’s KE can take on any value, thus there is a continuous spectra. Fixed amount of energy shared between the three particles.Total KE of the three particles determined by where m=mass difference before and after decay. (E is NOT difference between two nuclear energy levels, that is for gamma, not beta decay)Energy of the gamma photon is determined by the difference between the two nuclear energy levels.Gamma photon: Discrete energies corresponding to difference between two nuclear energy levels (excited nucleus and ground state). Small deflection in magnetic field.Large deflection in magnetic fieldNo deflection in magnetic fieldStrong ionizing ability. Alpha particle heavy enough to ‘knock’ out electrons from atoms during collision.Weak ionizing ability. Beta particle is lighter compared to alpha particle. (Ionizing property allows radiation to be detected)Weakest ionizing ability.Be prepared to draw nuclear energy level diagrams of radioactive decay (don’t forget gamma decay from excited to ground state!)Biological effects of Ionizing Radiation:- Cause molecular damage to biologically important molecules e.g. DNA, RNA etc., may cause them to cease functioning, die or prevent from reproduction- Ionization of surrounding medium may interfere with complex chemical reactions e.g. metabolic pathways- Damage cells in body tissues, cause growth of malignant cells (cancer)Nuclear Stability:Above the band of stability: Too many neutrons compared to protons, undergo alpha (removes neutrons) or beta minus (adds protons) decay.Below the band of stability: Too many protons compared to neutrons, undergo beta positive (adds neutrons) decay.*Extra neutrons are needed for stability of high-Z (proton number) nuclei, as Coulomb force is long-range while nuclear force is short-ranged.Transmutation: A nuclear reaction where a nucleus is struck by another nucleus or particle, and is transformed into a different particle.(Neutrons are usually used in nuclear reactions as they have no charge and therefore are not repelled by the nucleus) Distinguish from fusion and fission. Artificial and natural transmutation.Mass defect: Difference between total mass of the constituents of a nucleus and the mass of nucleus. This mass defect has become energy released during the formation of the nucleus in the form of radiation or kinetic energy. (a measure of the binding energy)Binding energy: The amount of energy released when a nucleus is assembled from its component nucleons.Binding energy per nucleon: The amount of energy released when a nucleus is assembled from its component nucleons, divided by the number of nucleons making up the nucleus.(Greater binding energy à Nucleus is more stable. Hence reaction is energetically feasible if products have greater BE per nucleon compared to reactants; products are more stable)For spontaneous nuclear reaction from AàB, change from unstable state to more stable state, binding energy per nucleon of B is greater than A.Energy released = BEproduct – (BEreactant A + BEreactant B)BEproduct = BEreactant A + BEreactant B – Energy releasedEnergy is released in the form of kinetic energy.Nuclear fission: When heavy nuclei disintegrate into two or more smaller, stable nuclei. (Occurs for nuclei with high A/nucleon/mass number)In nuclear reactors: Nuclear fission occurs, large energy release. Resulting smaller nuclei with fewer neutrons, hence neutrons released during reaction as well, and can be used to induce fission in other nuclei, causing a chain reaction.Uranium and plutonium-239 can be used as fuels in nuclear reactors.Nuclear fusion: When two or more light nuclei combine to form a heavier, more stable nuclei. (Occurs for nuclei with low A/nucleon/mass number)In the sun: Changing of hydrogen into helium in the sun, and example of nuclear fusion with large energy release. Hydrogen nuclei fuse together to form helium.Explain in terms of the no. of nucleons and the forces between them, why argon 36 is stable and argon 39 is radioactive. Both have same number of protons but different number of neutrons. Strong nuclear and coulomb force between nucleons. In Ar-36, nuclear force attraction and coulomb repulsion balanced therefore nucleus stable. However in Ar-39 there are excess neutrons, leads to imbalance in forces thus nucleus unstable.

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