valence shell

Examples of valence shell in the following topics:

• Multielectron Atoms

  • However, when more electrons are involved, each electron (in the $n$-shell) feels not only the electromagnetic attraction from the positive nucleus, but also repulsion forces from other electrons in shells from '1' to '$n$'.
  • This causes the net force on electrons in the outer electron shells to be significantly smaller in magnitude.
  • The shielding theory also explains why valence shell electrons are more easily removed from the atom.
  • Each has 10 electrons, and the number of nonvalence electrons is two (10 total electrons minus eight valence electrons), but the effective nuclear charge varies because each has a different number of protons:

• Electron Configurations

  • The outermost electron shell is often referred to as the valence shell and (to a first approximation) determines the chemical properties.

• The Periodic Table of Elements

  • (The terminology of s-, p-, and d- blocks originate from the valence atomic orbitals the element's electrons occupy. ) Some groups have specific names, such as the halogens or the noble gases.
  • Modern quantum mechanical theories of atomic structure explain group trends by proposing that elements in the same group generally have the same electron configurations in their valence (or outermost, partially filled) shell.

• Gravitational Attraction of Spherical Bodies: A Uniform Sphere

  • The gravitational force acting by a spherically symmetric shell upon a point mass inside it, is the vector sum of gravitational forces acted by each part of the shell, and this vector sum is equal to zero.
  • That is, a mass $m$ within a spherically symmetric shell of mass $M$, will feel no net force (Statement 2 of Shell Theorem).
  • We can use the results and corollaries of the Shell Theorem to analyze this case.
  • The contribution of all shells of the sphere at a radius (or distance) greater than $d$ from the sphere's center-of-mass can be ignored (see above corollary of the Shell Theorem).
  • This diagram outlines the geometry considered when proving The Shell Theorem.

• Nuclear Stability

  • The stability of an atom depends on the ratio and number of protons and neutrons, which may represent closed and filled quantum shells.
  • The stability of an atom depends on the ratio of its protons to its neutrons, as well as on whether it contains a "magic number" of neutrons or protons that would represent closed and filled quantum shells.
  • These quantum shells correspond to energy levels within the shell model of the nucleus.
  • Filled shells, such as the filled shell of 50 protons in the element tin, confers unusual stability on the nuclide.

• Spin-Orbit Coupling

  • The value of $C$ can be positive (shells less than half-full) or negative (shells more than half-full).
  • Notice that we recover the result for hydrogen; the $2p$ shell is clearly less than half-full.
  • We can make sense of the situation of a nearly full shell but realizing that a completely full shell is spherically symmetric so a nearly full level acts as if it has a few holes whose charge and magnetic moment have the opposite sign of an electrons.

• Ferromagnetism

  • However, in materials with a filled electron shell, the total dipole moment of the electrons is zero, as the spins are in up/down pairs.
  • Only atoms with partially filled shells (i.e., unpaired spins) can have a net magnetic moment.
  • Thus ferromagnetism only occurs in materials with partially filled shells.
  • (According to Hund's rules, the first few electrons in a shell tend to have the same spin, thereby increasing the total dipole moment. )

• X-Rays

  • X-ray fluorescence, if the electron has enough energy that it can knock an orbital electron out of the inner electron shell of a metal atom.
  • Usually these are transitions from upper shells into the K shell (called K lines), or the L shell (called L lines), and so on.

• Oscillator Strengths

  • If there is a closed shell of electrons we can focus on just the $q$ electrons in the open shell to get

• Problems

  • How much energy does a photon need to ionize the following atoms by removing a K-shell electron?