Positron Emission in C#.NET

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Positron Emission
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A positron is essentially an electron that has a positive charge instead of a negative one It is represented as 0 or 0 e Positron emission results from the conversion of a proton to 1 1 1 1 0 a neutron and a positron: +1 p 0 n + +1 e It is observed in the decay of some natural radioactive isotopes, such as K-40:
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Electron Capture
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Ar + +0 e 1
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The four decay modes described above all involve the emission or giving off of a particle; electron capture is the capturing of an electron from the energy level closest to the nucleus 0 1 1 (1s) by a proton in the nucleus This creates a neutron: 1 e + 1 p 0 n Electron capture leaves a vacancy in the 1s energy level, and an electron from a higher energy level drops down to fill this vacancy A cascading effect occurs as the electrons shift downward and, as they do so, energy is released This energy falls in the X-ray part of the electromagnetic spectrum These X-rays give scientists a clue that electron capture has taken place Polonium-204 undergoes electron capture:
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Po + 0 e 1
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Bi + X-rays Notice that
the atomic number has decreased by 1, but the mass number has remained the same Remember that electron capture is the only decay mode that involves adding a particle to the left side of the reaction arrow
Nuclear Stability
KEY IDEA
Predicting whether a particular isotope is stable and what type of decay mode it might undergo can be tricky All isotopes containing 84 or more protons are unstable and will undergo nuclear decay For these large, massive isotopes, alpha decay is observed most commonly Alpha decay gets rid of four units of mass and two units of charge, thus helping to relieve the repulsive stress found in these nuclei For other isotopes, with atomic numbers less than 84, stability is best predicted by the use of the neutron-to-proton (n/p) ratio If one plots the number of neutrons versus the number of protons for the known stable isotopes, the nuclear belt of stability is formed At the low end of this belt of stability (Z < 20), the n/p ratio is 1 At the high end (Z 80), the n/p ratio is about 15 One can then use the n/p ratio of the isotope under question to predict whether or not it will be stable If it is unstable, the isotope will utilize a decay mode that will bring it back onto the belt of stability For example, consider Ne-18 It has 10 p and 8 n, giving a n/p ratio of 08 That is less than 1, so the isotope is unstable This isotope is neutron-poor, meaning it doesn t have
Nuclear Chemistry 263
enough neutrons (or has too many protons) to be stable Decay modes which increase the number of neutrons, decrease the number of protons, or both, would be favored Both positron emission and electron capture accomplish this by converting a proton into a neutron As a general rule, positron emission occurs with lighter isotopes and electron capture with heavier isotopes Isotopes that are neutron-rich, that have too many neutrons or not enough protons, lie above the belt of stability and tend to undergo beta emission because that decay mode converts a neutron into a proton A particular isotope may undergo a series of nuclear decays until finally a stable isotope is formed For example, radioactive U-238 decays to stable Pb-206 in 14 steps, a majority of which are alpha emissions, as one might predict
Nuclear Decay Calculations
A radioactive isotope may be unstable, but it is impossible to predict when a certain atom will decay However, if a statistically large enough sample is examined, some trends become obvious The radioactive decay follows first-order kinetics (see 14 for a more in-depth discussion of first-order reactions and equations) If the number of radioactive atoms in a sample is monitored, it can be determined that it takes a certain amount of time for half the sample to decay; it takes the same amount of time for half the remaining sample to decay; and so on The amount of time it takes for half the sample to decay is called the half-life of the isotope and is given the symbol t1/2 The table below shows the percentage of radioactive isotope remaining versus half-life
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