Stability nuclear

Nuclear Stability.—Two good reviews of the theoretical predictions of nuclear stability in the superheavy region have been published. One is a very readable account by Nix, whereas a more comprehensive survey is given by Johansson, et al. Readers who require more detail are referred to the latter in particular. Somewhat earlier reviews came from Nilsson and Strutinsky.  

This is perhaps not an appropriate place to consider nuclear theory in detail, but some of the results of theoretical calculations must be given, as these predictions are of course the very bedrock on which all expectations of discovering superheavy elements are built. 

Identify the missing species X in each of the following nuclear equations  

Strategy Determine the mass number for the unknown species, X, by summing the mass numbers on both sides of the equation  

S reactant mass numbers = S product mass numbers 

Similarly, determine the atomic number for the unknown species  

reactant atomic numbers = 2 product atomic numbers 

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 1.5. 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 0.8. That is less than 1, so the isotope is unstable. This isotope is neutron-poor, meaning it doesn t have 

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. 

Sometimes it is difficult to predict if a particular isotope is stable and, if unstable, what type of decay mode it might undergo. All isotopes that contain 84 or more protons are unstable. These unstable isotopes will undergo nuclear decay. For these large massive isotopes, we observe alpha decay 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 the nucleus of these isotopes. For other isotopes of atomic number less than 83, we can best predict stability by the use of the neutron to proton (n/p) ratio. 

Consider neon-18 or Ne-18. It has lOp and 8n, giving an n/p ratio of 0.8. For a light isotope, like this one, this value is low. A low value indicates that this isotope will probably be unstable. Neutron-poor isotopes, meaning that it has a low n/p ratio do not have enough neutrons (or has too many protons) to be stable. Decay modes that increase the number of neutrons and/or decrease the number of protons are favorable. Both positron emission and electron capture accomplish this by converting a proton into a neutron. As a rule, positron emission occurs with lighter isotopes and electron capture with heavier ones. 

The atomic number, Z, is the number of protons in the nucleus. Both the proton and neutron have masses that are approximately 1 atomic mass unit, amu. The electron has a mass of only about 1/1837 of the proton or neutron, so almost all of the mass of the atoms is made up by the protons and neutrons. Therefore, adding the number of protons to the number of neutrons gives the approximate mass of the nuclide in amu. That number is called the mass number and is given the symbol A. The number of neutrons is found by subtracting the atomic number, Z, from the mass number, A. Frequently, the number of neutrons is designated as N and (A - Z) = N. In describing a nuclide, the atomic number and mass number are included with the symbol for the atom. This is shown for an isotope of X as AZX. 

2 reactant mass numbers = 2 product mass numbers Similarly, determine the atomic number for the unknown species  

2 reactant atomic numbers = 2 product atomic numbers Use the mass number and atomic number to determine the identity of the unknown species. 

Think About It The rules of summation we apply to balance nuclear equations can be thought of 

Download mini lecture videos for key concept review and exam prep from OWL or purchase them from www.cengagebrain.com 

As we have learned from Chapter 2, atomic nuclei consist of protons, which are positively charged, and neutrons, which have zero charge. According to classical electrostatics, we should expect the protons to repel one another and the nucleus to fly apart. It turns out, however, that at the very short distances of separation characteristic of atomic nuclei (about 10 m), there are strong attractive forces between nuclear particles. The stability of a nucleus depends upon the balance between these forces and electrostatic repulsion. 

Despite extensive research, we still do not have a clear understanding of the way in which those forces lead to nuclear stability. All we have is a series of empirical rules for predicting which nuclei will be most stable. The most important of these rules are listed below. 

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Since the radioactive half-lives of the known transuranium elements and their resistance to spontaneous fission decrease with increase in atomic number, the outlook for the synthesis of further elements might appear increasingly bleak. However, theoretical calculations of nuclear stabilities, based on the concept of closed nucleon shells (p. 13) suggest the existence of an island of stability around Z= 114 and N= 184. Attention has therefore been directed towards the synthesis of element 114 (a congenor of Pb in Group 14 and adjacent superheavy elements, by bombardment of heavy nuclides with a wide range of heavy ions, but so far without success. 

Click Coached Problems for a self-study module on nuclear stability. 

Beta radiation Electron emission from unstable nuclei, 26,30,528 Binary molecular compound, 41-42,190 Binding energy Energy equivalent of the mass defect measure of nuclear stability, 522,523 Bismuth (m) sulfide, 540 Blassie, Michael, 629 Blind staggers, 574 Blister copper, 539 Blood alcohol concentrations, 43t Body-centered cubic cell (BCC) A cubic unit cell with an atom at each comer and one at the center, 246 Bohrmodd Model of the hydrogen atom... 

Radioactivity The ability possessed by some natural and synthetic isotopes to undergo nuclear transformation to other isotopes, 513 applications, 516-518 biological effects, 528-529 bombardment reactions, 514-516 diagnostic uses, 516t discovery of, 517 modes of decay, 513-514 nuclear stability and, 29-30 rate of decay, 518-520,531q Radium, 521-522 Radon, 528 Ramsay, William, 190 Random polymer 613-614 Randomness factor, 452-453 Raoult s law A relation between the vapor pressure (P) of a component of a solution and that of the pure component (P°) at the same temperature P — XP°, where X is the mole fraction, 268... 

The outstanding characteristic of the actinide elements is that their nuclei decay at a measurable rate into simpler fragments. Let us examine the general problem of nuclear stability. In Chapter 6 we mentioned that nuclei are made up of protons and neutrons, and that each type of nucleus can be described by two numbers its atomic number (the number of protons), and its mass number (the sum of the number of neutrons and protons). A certain type of nucleus is represented by the chemical symbol of the element, with the atomic number written at its lower left and the mass number written at its upper left. Thus the symbol... 

It is relatively easy to summarize how nuclear stability (and hence the attractive nuclear forces) depends upon the numbers of protons and neutrons in the nucleus. For atoms with atomic number less than 20, the most stable nuclei are those in which there are equal numbers of protons and neutrons. For atoms with atomic numbers between 20 and 83, the most stable nuclei have more neutrons than protons. For atoms of atomic number greater than 83, no nucleus can be considered stable by our definition. These... 

The pattern of nuclear stability can be used to predict the likely mode of radioactive decay neutron-rich nuclei tend to reduce their neutron count proton-rich nuclei tend to reduce their proton count. In general, only heavy nuclides emit a particles. 

C02-0025. Write a paragraph summarizing nuclear stability and instability. 

C22-0029. Write a paragraph summarizing the important features of each of the following topics (a) nuclear stability (b) nuclear decay (c) fission (d) fusion and (e) binding energy. 

Nuclear reactions Nuclear stability Half-lives (ti/2)... 

Know that nuclear stability is best related to the neutron-to-proton ratio (n/p), which starts at about 1/1 for light isotopes and ends at about 1.5/1 for heavier isotopes with atomic numbers up to 83- All isotopes of atomic number greater than 84 are unstable and will commonly undergo alpha decay. Below atomic number 84, neutron-poor isotopes will probably undergo positron emission or electron capture, while neutron-rich isotopes will probably undergo beta emission. 

In this book the superactinide elements begin at Z-114 because this is the first element that was recognized in what is known as the island of stability, also referred to as the Island of Nuclear Stability. The stability of Z-114 is related to its exceptional long half-life of 30 seconds, which provides adequate time for detection and research on it. It also appears that the heavier the element, the shorter its half-life. 

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