Neutrons energy shells

Electron capture has the same effect as positron emission. In this process, an electron from an inner energy shell (especially the Is orbital) is captured by the nucleus. The captured electron is used to convert a proton into a neutron. This conversion can be shown thus ... 

These numbers explain the shape of the periodic table. Each element has one more electron (and one more proton and perhaps more neutrons) than the one before. At first the lowest energy shell (n = 1) is filled. There is only one orbital, Is, and we can put one or two electrons in it. There are therefore two elements in this block, H and He. Next we must move to the second shell ( = 2), filling 2s first so we start the top of groups 1 and 2 with Li and Be. These occupy the top of the red stack marked s block because all the elements in this block have one or two electrons in their outermost s orbital and no electrons in the outermost p orbital. Then we can start on the 2p orbitals. There are three of these so we can put in six electrons and get six elements B, C, N, O, F, and Ne. They occupy the top row of the black p block. Most of the elements we need in this book are in those blocks. Some, Na, K, and Mg for example, are in the s block and others, Si, P, and S for example, are in the second row of the p block. 

Protons and neutrons reside in energy shells, just as electrons do. This fact limits the number of protons and neutrons that a nucleus can have and still remain stable. 

Matter is composed of atoms. An atom consists of a nucleus containing protons (Z) and neutrons (N), collectively called nucleons, and electrons rotating around the nucleus. The sum of neutrons and protons (total number of nucleons) is the mass number denoted by A. The properties of neutrons, protons, and electrons are listed in Table 1.1. The number of electrons in an atom is equal to the number of protons (atomic number Z) in the nucleus. The electrons rotate along different energy shells designated as A -shcll, L-shell, M-shell, etc. (Fig. 1.1). Each shell further consists of subshells or orbitals, e.g., the L-shell has s orbital the L-shell has s and p orbitals the M-shell has s, p, and d orbitals, and the A-shell has s, p, d, and / orbitals. Each orbital can accommodate only a limited number of electrons. For example, the s orbital contains up to 2 electrons the p orbital, 6 electrons the d orbital, 10 electrons and the / orbital, 14 electrons. The capacity number of electrons in each orbital adds up to give the maximum number of electrons that each energy shell can hold. Thus, the L-shell contains 2 electrons the L-shell 8 electrons, the M-shell 18 electrons, and so forth. 

Fig. 25 a and b. (a) Arrangement for measurement of nonelastic cross sections with spherical shell surrounding the source (S). This method requires a neutron source for which both the yield and neutron energy do not vary with the angle of emission, (b) Arrangement for measurement of nonelastic cross sections with spherical shell surrounding the detector (U). 

Taking into account the success of the spherical and deformed shell models, it is tempting to calculate the total energy of nucleus by summation of single-particle proton and neutron energies up to the Fermi level. Then... 

O Figure 2.12a shows the theoretical single-neutron energies (e, staircase function) versus neutron number (N)- The smooth, average curve e (N )removes local fluctuations. The shell... 

Atoms consist of electrons and protons in equal numbers and, in all cases except the hydrogen atom, some number of neutrons. Electrons and protons have equal but opposite charges, but greatly different masses. The mass of a proton is 1.67 X 10 24 grams. In atoms that have many electrons, the electrons are not all held with the same energy later we will discuss the shell stmcture of electrons in atoms. At this point, we see that the early experiments in atomic physics have provided a general view of the structures of atoms. 

Scientists have known that nuclides which have certain "magic numbers" of protons and neutrons are especially stable. Nuclides with a number of protons or a number of neutrons or a sum of the two equal to 2, 8, 20, 28, 50, 82 or 126 have unusual stability. Examples of this are He, gO, 2oCa, Sr, and 2gfPb. This suggests a shell (energy level) model for the nucleus similar to the shell model of electron configurations. 

Fig. 2.2. Energy levels for ISW and 3DHO potentials. Each shows major gaps corresponding to closed shells and the numbers in circles give the cumulative number of protons or neutrons allowed by the Pauli principle. In a more realistic potential, the levels for given (n, T) are intermediate between these extremes, in which the lower magic numbers 2, 8 and 20 are already apparent. Adapted from Krane(1987).

These shell closures have a profound influence on nuclear properties, in particular the binding energy (adding terms not accounted for in Eq. 2.2), particle separation energies and neutron capture cross-sections. The shell model also forms a basis for predicting the properties of nuclear energy levels, especially the ground... 

Electron capture, in which an inner-shell electron is captured by a proton in the nucleus with the formation of a neutron. X-rays are emitted as the electrons cascade down to fill the vacancy in the lower energy level. 

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