electron shell

Examples of electron 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.
  • Therefore, these electrons are not as strongly bonded to the nucleus as electrons closer to the nucleus.
  • 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 electron configuration is the distribution of electrons of an atom or molecule in atomic or molecular orbitals.
  • The electron configuration is the distribution of electrons of an atom or molecule in atomic or molecular orbitals.
  • Electron configurations describe electrons as each moving independently in an orbital, in an average field created by all other orbitals.
  • However, the electronic wave function is usually dominated by a very small number of configurations and therefore the notion of electronic configuration remains essential for multi-electron systems.
  • The outermost electron shell is often referred to as the valence shell and (to a first approximation) determines the chemical properties.

• Ferromagnetism

  • Thus, an electron itself behaves as a tiny magnet.
  • 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

  • The high-velocity electrons collide with a metal target, the anode, creating the x-rays.
  • When the electrons hit the target, x-rays are created through two different atomic processes:
  • 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.
  • As a result, electrons from higher energy levels fill up the vacancy, and x-ray photons are emitted.
  • 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

  • where $N $ is the total number of electrons in the atom and the summation is over all the states.
  • If there is a closed shell of electrons we can focus on just the $q$ electrons in the open shell to get
  • where the sum is over transitions that involve the outermost electrons.

• Problems

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

• Basic Assumptions of the Bohr Model

  • He suggested that electrons could only have certain classical motions:
  • These orbits are associated with definite energies and are also called energy shells or energy levels.
  • In these orbits, the electron's acceleration does not result in radiation and energy loss as required by classical electrodynamics.
  • The Rutherford–Bohr model of the hydrogen atom ($Z= 1$) or a hydrogen-like ion ($Z>1$), where the negatively charged electron confined to an atomic shell encircles a small, positively charged atomic nucleus, and where an electron jump between orbits is accompanied by an emitted or absorbed amount of electromagnetic energy ($h\nu$).
  • The orbits in which the electron may travel are shown as gray circles; their radius increases as $n^2$, where $n$ is the principal quantum number.

• The Bohr Model of the Atom

  • Bohr suggested that electrons in hydrogen could have certain classical motions only when restricted by a quantum rule.
  • Because the electron would lose energy, it would gradually spiral inwards, collapsing into the nucleus.
  • Also, as the electron spirals inward, the emission would gradually increase in frequency as the orbit got smaller and faster.
  • He suggested that electrons could only have certain classical motions:
  • These orbits are associated with definite energies and are also called energy shells or energy levels.

• The Periodic Table of Elements

  • A periodic table is a tabular display of elements organized by their atomic numbers, electron configurations, and chemical properties.
  • The elements are organized based on their atomic numbers, electron configurations, and recurring chemical properties.
  • 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.
  • Elements in the same period show trends in atomic radius, ionization energy, and electron affinity.
  • This occurs because each successive element has an added proton and electron, which causes the electron to be drawn closer to the nucleus, decreasing the radius.

• Spin-Orbit Coupling

  • Let's imagine that we move into the frame of the electron, we are moving through an electric field so there is a magnetic field
  • The electron has a magnetic moment of
  • 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.