Effective Nuclear Charge

7 Key excerpts on "Effective Nuclear Charge"

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  eBook - PDF

  Chemistry

  The Molecular Nature of Matter

  • Neil D. Jespersen, Alison Hyslop(Authors)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  The amount of positive charge felt by the valence electrons of an atom is the Effective Nuclear Charge. This is less than the actual nuclear charge because core electrons partially shield the valence electrons from the full positive charge of the nucleus. Atomic radii depend on the value of n of the valence shell orbitals and the Effective Nuclear Charge experienced by the valence electrons. Atomic radii decrease from left to right in a period and from bottom to top in a group in the periodic table. Negative ions are larger than the atoms from which they are formed; positive ions are smaller than the atoms from which they are formed. Ionization energy (IE) is the energy needed to remove an elec- tron from an isolated gaseous atom, molecule, or ion in its ground state; it is endothermic. The first ionization energies of the elements increase from left to right in a period and from bottom to top in a group. (Irregularities occur in a period when the nature of the orbital from which the electron is removed changes and when the electron removed is first taken from a doubly occupied p orbital.) Successive ionization energies become larger, but there is a very large jump when the next electron must come from the noble gas core beneath the valence shell. Electron affinity (EA) is the potential energy change asso- ciated with the addition of an electron to a gaseous atom or ion in its ground state. For atoms, the first EA is usually exothermic. When more than one electron is added to an atom, the overall potential Review Questions 359 energy change is endothermic. In general, electron affinity becomes more exothermic from left to right in a period and from bottom to top in a group.

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  A Concise Handbook of Mathematics, Physics, and Engineering Sciences

  • Andrei D. Polyanin, Alexei Chernoutsan(Authors)
  • 2010(Publication Date)
  • CRC Press

    (Publisher)

  Chapter P8 Elements of Nuclear Physics The idea that practically the entire mass of an atom is concentrated in its positively charged nucleus of infinitesimally small dimensions is due to Rutherford’s experiments (see Chap-ter P6). Since the dimensions of nuclei turned out to be by five orders less than those of atoms, it can be assumed, in the framework of atomic physics, that the nucleus is a point Coulomb center. Actually, the nucleus is a complex structure formed by strongly interacting particles (several ones or hundreds) obeying the laws of quantum mechanics and quantum statistics. The nuclei can undergo radioactive transformations, participate in nuclear reac-tions, disintegrate, and merge with other nuclei. The characteristic energies in that nuclear world are measured in millions of electron-volts, which explains why nuclei appear as stable objects in atomic processes with energies up to several hundred electron-volts. P8.1. Basic Properties of Nuclei P8.1.1. Characteristics of Nuclei ◮ Nuclear Composition. The atomic nucleus consists of protons and neutrons—particles collectively named nucleons . The proton is a subatomic particle with positive charge e and mass m p = 1836 . 15 m e , where m e is the electron mass. The neutron is an electrically neutral particle whose mass is slightly greater than that of the proton: m n = 1838 . 68 m e . In its free state, the neutron is unstable in the sense that within 15.5 minutes, on the average, it turns into a proton after emitting an electron and an antineutrino: n → p + e + tildewide ν . The spin* of both the proton and neutron is equal to 1 / 2 , which means that they belong to the class of fermions. Both the proton and the neutron possess nonzero magnetic moments: μ p = 2 . 793 μ N and μ n = – 1 . 91 μ N , where μ N = e planckover2pi1 / 2 m p is the so-called nuclear magneton ( μ N = μ B / 1836 . 15 ).

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  An Introduction to Nuclear Physics

  • W. N. Cottingham, D. A. Greenwood(Authors)
  • 2001(Publication Date)
  • Cambridge University Press

    (Publisher)

  tions of the strong nuclear interaction are not present, and the weak interaction is negligible for the scattering process. The most significant interaction between a charged lepton, which can be regarded as a struc-tureless point object, and the nuclear charge is the Coulomb force, and this is well understood. If the nucleus has a magnetic moment, the mag-netic contribution to the scattering becomes important at large scattering angles, but this also is well understood. If scattering experiments are to give detailed information on the nuclear charge distribution, it is clear that the de Broglie wavelength of the incident particle must be less than, or at least comparable with, the distances over which the nuclear charge density changes. An electron with = 2 † 1 fm has momentum p ˆ 2 » = and hence energy E ˆ p 2 c 2 ‡ m 2 c 4 † 1 2 200 MeV. At these energies, the electrons are described by the Dirac relativistic wave-equation, rather than by the SchroÈ dinger equation. The experiments yield a differential cross-section d E ; † = d (Appendix A) for elastic scattering from the nucleus through an angle , which depends on the energy E of the incident electrons. Typical experimental data are shown in Fig. 4.1. The incident electrons are, of course, also scattered by the atomic electrons in the target. However, this scattering is easily distinguished from the nuclear scattering by the lower energy of the scattered electrons. Whereas the recoil energy taken up by the heavy nucleus is very small, the recoil energy taken up by the atomic electrons is appreciable, except for scattering in the forward direction. (See Problem 4.1.) The nuclear charge density will be described by some density function e ch r † .

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  Poetry Of Physics And The Physics Of Poetry, The

  • Robert K Logan(Author)
  • 2010(Publication Date)
  • World Scientific

    (Publisher)

  Much has been learned about the nuclear force by studying the scattering of protons by protons. We shall discuss this interaction in greater detail in the next chapter on elementary particles. For the purpose of discussing nuclear physics the above description of the nuclear force will suffice. Nuclear Binding Energy One of the earliest indications of the strength of the nuclear force was the size of the nuclear binding energy compared with atomic binding energy. If two particles form a bound state due to an attractive force, then the 228 The Poetry of Physics and The Physics of Poetry total mass of the bound state is less than the sum of the masses of the individual particles composing the system. The reason for this is that the potential energy of the bound particles is negative. If one wished to separate the two particles, one would have to supply energy to do work against the attractive force, hence the negative potential energy. The rest mass energy of the bound state is less than that of the sum of the rest mass energies of the individual components making up the bound state because of the negative potential energy and because as Einstein discovered mass and energy are equivalent. In fact the attenuation of nuclear mass due to binding energy formed one of the basic tests of Einstein’s hypothesis of the equivalence of mass and energy. The binding energy of the electron in the hydrogen atom is only 13.6 electron volts (eV). An eV is a unit of energy equal to the energy an electron gains when accelerated through a one volt potential. The eV is the commonest unit of energy in nuclear and elementary particle physics. Rest mass energies are also measured in electron volts or eVs. Since mass and energy are equivalent, one can specify the mass of a particle by specifying the energy of the particle’s rest mass, which is equal to mc 2 and is measured in eVs or MeVs (million electron volts).

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  Modern Physics for Scientists and Engineers

  • Stephen Thornton, Andrew Rex, Carol Hood, , Stephen Thornton, Stephen Thornton, Andrew Rex, Carol Hood(Authors)
  • 2020(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  Equal numbers of neutrons and protons may give the most attractive aver- age internucleon nuclear force, but the Coulomb force must be considered as well. As the number of protons increases, the Coulomb repulsion among all the protons becomes stronger and stronger until it eventually affects the binding. The electrostatic energy required to contain a charge Ze evenly spread through- out a sphere of radius R can be calculated by determining the work required to bring the charge inside the sphere from infinity (see Problem 61) and is determined to be DE Coul 5 3 5 (Ze) 2 4pe 0 R (12.17) Line of stability Copyright 2021 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 448 Chapter 12 The Atomic Nucleus For a single proton, Equation (12.17) gives for the self-energy DE Coul 5 3 5 e 2 4pe 0 R This term represents the work done to assemble the proton itself, and we do not want to include it in the electrostatic self-energy of a nucleus composed of Z protons. Therefore we must subtract Z such terms from the total given in Equa- tion (12.17) to give us the total Coulomb repulsion energy in a nucleus: DE Coul 5 3 5 Z(Z 2 1)e 2 4pe 0 R (12.18) Figure 12.6 A plot of the known nuclides with neutron number N versus proton num- ber Z . The solid points repre- sent stable nuclides, and the shaded area represents unsta- ble nuclei. A smooth line through the solid points would represent the line of stability.

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  eBook - ePub

  Biophysical Basis of Physiology and Calcium Signaling Mechanism in Cardiac and Smooth Muscle

  • Tetsuya Watanabe(Author)
  • 2018(Publication Date)
  • Academic Press

    (Publisher)

  The shielding occurs between multielectrons. Each electron experiences the different pull from the nucleus depending on how they are close to the nucleus relative to the other. One electron closer to the nucleus shields the other electron from the nucleus.

  3.5 Shielding Effect and Effective Atomic Number of He Atom

  Taking two extreme possible locations of two electrons of He atom, we consider the shielding effect and effective atomic number of He atom for both cases.

  Extreme case #1: If electron #2 is very close to the nucleus and electron #1 is very far from the nucleus, electron #1 experiences a minimum attractive force exerted by Z eff  = + 1 instead of + 2 of He atom. Because electron #2 shields electron #1 from a positive charge of one proton in the He nucleus, the orbital energy of electron #1 (E

  e  # 1

  ) is considered as the orbital energy of one electron H atom (Fig. 3.2 ). Z eff denotes the effective atomic number .

  Fig. 3.2 Electron #2 shields electron #1 from a positive charge of one proton in the He nucleus. Electron #1 feels a pull by only one remaining proton in He nucleus.

  E

  e # 1

  = −

  IE

  e # 1

  = −

  Z eff

  2

  K

  n 2

  = −

  + 1

  2

  1 2

  K = − 2.18 ×

  10

  − 18

  J

  Ionization energy (IE ) is the minimum energy required to remove an electron from an atom.

  Extreme case #2: If electron #1 close to the nucleus and electron #2 is very far from the nucleus, electron #1 experiences a maximum force exerted by Z eff  = + 2  instead of + 1 because of no shielding effect.

  E

  e # 1

  = −

  IE

  e # 1

  = −

  Z eff

  2

  K

  n 2

  = −

  + 2

  2

  1 2

  K = − 8.72 ×

  10

  − 18

  J

  Extreme case #1 indicates 100% shielding effect: Z eff  = + 1. IE

  e  # 1

   = 2.18 × 10− 18 J.

  Extreme case #2 indicates no shielding effect: Z eff  = + 2. IE

  e  # 1

   = 8.72 × 10− 18 J.

  Experimentally determined IE

  He

  is 3.94 × 10− 18 J that is a result of the shielding effect between 0% and 100%.

  Z eff  (n  = 1) is calculated from the experimentally determined IE

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  eBook - ePub

  Atomic Physics: 8th Edition

  • Max Born(Author)
  • 2013(Publication Date)
  • Dover Publications

    (Publisher)

  Z, which gives the nuclear charge, is equal to the number which would be assigned to the element in question in a consecutive enumeration of the elements in the periodic system. If the atom is to be neutral, the number giving the nuclear charge must agree with the number of electrons in the electron cloud surrounding the nucleus, as determined by optical and X-ray scattering experiments. The chemical behaviour of the atom depends of course on the external electrons, so that it is not the mass of the atom, but its atomic number (or number giving the nuclear charge), which determines its chemical properties. Isotopes have the same atomic number.

  For collisions which are nearly central, i.e. for scattering through wide angles, deviations occur from the distribution of the scattered α-particles determined by Coulomb’s law. From this we must infer that Coulomb’s law only holds down to distances of about 10–13 cm. The nucleus also has a finite size; it is worthy of remark that the “nuclear radius” is of the same order of magnitude as the “radius of the electron”.

  According to Rutherford, the nuclear atom may be described as follows. In the centre of the atom there is the nucleus; this was thought of as composed of protons and electrons, but this assumption led to many difficulties, e.g. that of packing the electrons into the nuclear volume, which is of the same order as that of one electron (radius 10–13 cm.; see p. 49). Since the discovery of the neutron a more satisfactory model has been developed: viz. a nucleus composed of p protons and n neutrons; the nuclear charge number (atomic number) is then Z = p, the atomic mass number is A = p + n. The considerations in favour of this model will be presented immediately (§ 4 , p. 64).

  Round the nucleus, as has been mentioned, there move in the neutral atom Z electrons, which fill a sphere of radius ∼ 10–8

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