Stability of nuclei

The nucleus is not involved in normal chemical reactions. In radioactivity, it is the nucleus that is undergoes the changes. Nuclear forces are extremely strong forces that hold the nuclear particles together. These forces make the nucleus very stable. Remember that the protons are positively charged and can exert repulsive forces among themselves. It has been found out that there are certain predictable behavioral patterns in elements as the atomic number increases. As the atomic number increases, the neutron-to-proton ratio increases and as more and more protons are present in the nucleus, the stabilizing forces are not sufficient to keep the nucleus stable. Thus the stability of the nucleus decreases as the neutron-to-proton ratio increases. 

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Nuclear Stability n/p ratio The stability of nucleus depends on the number of neutrons and protons present. Light... 

Two factors affect the stability of this orbital. The first is the stabilizing influence of the positively charged nuclei at the center of the AOs. This factor requires that the center of the AO be as close as possible to the nucleus. The other factor is the stabilizing overlap between the two constituent AOs, which requires that they approach each other as closely as possible. The best compromise is probably to shift the center of each AO slightly away from its own nucleus towards the other atom, as shown in figure 7-23a. However, these slightly shifted positions are only correct for this particular MO. Others may require a slight shift in the opposite direction. 

A guide to tire stabilities of inter-metallic compounds can be obtained from the semi-empirical model of Miedema et al. (loc. cit.), in which the heat of interaction between two elements is determined by a contribution arising from the difference in work functions, A0, of tire elements, which leads to an exothermic contribution, and tire difference in the electron concentration at tire periphery of the atoms, A w, which leads to an endothermic contribution. The latter term is referred to in metal physics as the concentration of electrons at the periphery of the Wigner-Seitz cell which contains the nucleus and elecUonic structure of each metal atom within the atomic volume in the metallic state. This term is also closely related to tire bulk modulus of each element. The work function difference is very similar to the electronegativity difference. The equation which is used in tire Miedema treatment to... 

Benzoic Acid.—Tire o idation of the side-chains m aiomatic hydrocaibons is a mattei of considerable intci est, as illustrating the diffeience of stability of the side-chain and nucleus, and also the influence which the rehitive positions of the side-chains, where more than one is present, exeit in piescnce of oxidisiny agents. 

The acyl residue controls the formation and stability of the carbonium ion. If the carbonium ion is destabilized (by electron withdrawing groups), then cyclization to the phenanthridine nucleus will be sluggish. The slower the rate of cyclization, the greater the chance of side reactions with the cyclization reagent. Therefore, the yield of the phenanthridine will depend on the relative rates of cyclization and side reactions, which is controlled by the stability of the carbonium ion. 

What accounts for the stability of conjugated dienes According to valence bond theory (Sections 1.5 and 1.8), the stability is due to orbital hybridization. Typical C—C bonds like those in alkanes result from a overlap of 5p3 orbitals on both carbons. In a conjugated diene, however, the central C—C bond results from conjugated diene results in part from the greater amount of s character in the orbitals forming the C-C bond. 

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... 

In the previous section we saw that the stability of a nucleus is affected by its neutron/proton ratio. Even among those nuclei that we consider stable, however, there is a variation in the forces which hold the nucleus together. In order to study this variation in nuclear binding energy, let us consider the process of building a nucleus from protons and neutrons. For an example, let us look at the hypothetical reaction... 

Scheme 21 presents the successful sequence of reactions that solved the remaining two problems and led to the completion of the synthesis of cobyric acid. Exposure of 96 to concentrated sulfuric acid for one hour brings about a clean conversion of the nitrile grouping to the corresponding primary amide grouping. The stability of die corrin nucleus under these rather severe conditions is noteworthy. This new substance, intermediate 97, is identified as cobyrinic acid abcdeg hexamethylester f amide and it is produced along with a very similar substance which is epimeric to 97 at C-13. The action of sulfuric acid on 96 produces a diastereomeric... 

The high stability of porphyrins and metalloporphyrins is based on their aromaticity, so that porphyrins are not only most widespread in biological systems but also are found as geoporphyrins in sediments and have even been detected in interstellar space. The stability of the porphyrin ring system can be demonstrated by treatment with strong acids, which leave the macrocycle untouched. The instability of porphyrins occurs in reduction and oxidation reactions especially in the presence of light. The most common chemical reactivity of the porphyrin nucleus is electrophilic substitution which is typical for aromatic compounds. 

For each different element, there are a few specific values of A that result in stable nuclei. Figure 2-20 shows all the stable nuclei on a plot of the number of neutrons (iV) versus the number of protons (Z). These data show a striking pattern All stable nuclei fall within a belt of stability. Any nucleus whose ratio of neutrons to protons falls outside the belt of stability is unstable and decomposes spontaneously. Lighter nuclei lie along the JV = Z line, but the N jZ ratio of stable nuclei rises slowly until it reaches 1.54. The trend is illustrated by the N j Z... 

When Z gets big enough, no number of neutrons is enough to stabilize the nucleus. Notice in Figure 2-20 that there are no stable nuclei above bismuth, Z — 83. Some elements with higher Z are found on Earth, notably radium (Z = 88), thorium (Z = 90), and uranium (Z = 92), but all such elements are unstable and eventually disintegrate into nuclei with Z < 83. Consequently, the set of stable nuclei, those that make up the world of normal chemistry and provide the material for all terrestrial chemical reactions, is a small subset of all possible nuclei. 

An explanation of the direct 4s contribution to the charge density at the nucleus requires MO calculations. A simple MO diagram for octahedral complexes is shown in Fig. 4.4. The a-interaction of metal /-orbitals and symmetry-adapted ligand orbitals usually yields the major part to the stability of the bonds. According... 

Rather than giving the general expression for the Hellmann-Feynman theorem, we focus on the equation for a general diatomic molecule, because from it we can leam how p influences the stability of a bond. We take the intemuclear axis as the z axis. By symmetry, the x and y components of the forces on the two nuclei in a diatomic are zero. The force on a nucleus a therefore reduces to the z component only, Fz A, which is given by... 

As might be expected, substituents in the aromatic nucleus have a marked effect on the stability of ArN2 , electron-donating groups having a marked stabilising effect ... 

Radical attack on methylbenzene (toluene, 60) results in preferential hydrogen abstraction by Cl leading to overall substitution in the CH3 group, rather than addition to the nucleus. This reflects the greater stability of the first formed (delocalised) benzyl radical, PhCH2 (61), rather than the hexadienyl radical (62), in which the aromatic stabilisation of the starting material has been lost ... 

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