atomic orbital

Examples of atomic orbital in the following topics:

• 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.
  • In atoms, electrons fill atomic orbitals according to the Aufbau principle (shown in ), stated as: a maximum of two electrons are put into orbitals in the order of increasing orbital energy—the lowest-energy orbitals are filled before electrons are placed in higher-energy orbitals.
  • The molecular orbitals are labelled according to their symmetry, rather than the atomic orbital labels used for atoms and monoatomic ions: hence, the electron configuration of the diatomic oxygen molecule, O2, is 1σg2 1σu2 2σg2 2σu2 1πu4 3σg2 1πg2.
  • In the Aufbau Principle, as electrons are added to atoms, they are added to the lowest orbitals first.

• Quantum-Mechanical View of Atoms

  • Atom is a basic unit of matter that consists of a nucleus surrounded by negatively charged electron cloud, commonly called atomic orbitals.
  • Hydrogen-1 (one proton + one electron) is the simplest form of atoms, and not surprisingly, our quantum mechanical understanding of atoms evolved with the understanding of this species.
  • In 1913, physicist Niels Bohr suggested that the electrons were confined into clearly defined, quantized orbits, and could jump between these, but could not freely spiral inward or outward in intermediate states.
  • An electron must absorb or emit specific amounts of energy to transition between these fixed orbits.
  • Thereafter, the planetary model of the atom was discarded in favor of one that described atomic orbital zones around the nucleus where a given electron is most likely to be observed.

• The Bohr Model of the Atom

  • This atom model is disastrous, because it predicts that all atoms are unstable.
  • Also, as the electron spirals inward, the emission would gradually increase in frequency as the orbit got smaller and faster.
  • The electrons can only orbit stably, without radiating, in certain orbits (called by Bohr the "stationary orbits"): at a certain discrete set of distances from the nucleus.
  • These orbits are associated with definite energies and are also called energy shells or energy levels.
  • Niels Bohr, Danish physicist, used the planetary model of the atom to explain the atomic spectrum and size of the hydrogen atom.

• de Broglie and the Bohr Model

  • How does this affect electrons in atomic orbits?
  • When an electron is bound to an atom, its wavelength must fit into a small space, something like a standing wave on a string.
  • Not all orbits produce constructive interference and thus only certain orbits are allowed (i.e., the orbits are quantized).
  • This described electrons that were constrained to move about the nucleus of a hydrogen-like atom by being trapped by the potential of the positive nuclear charge.
  • I include a summary of the hydrogen atom's electronic structure and explain how an electron can interfere with itself in an orbit just like it can in a double-slit experiment.

• Basic Assumptions of the Bohr Model

  • To explain the puzzle, Bohr proposed what is now called the Bohr model of the atom in 1913.
  • The electrons can only orbit stably, without radiating, in certain orbits (called by Bohr the "stationary orbits") at a certain discrete set of distances from the nucleus.
  • These orbits are associated with definite energies and are also called energy shells or energy levels.
  • Here, Bohr explained the atomic hydrogen spectrum successfully for the first time by adopting a quantization condition and by introducing the Planck constant in his atomic model.
  • 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 ($h\nu$).

• Bohr Orbits

  • According to Bohr, electrons can only orbit stably, in certain orbits, at a certain discrete set of distances from the nucleus.
  • As we've seen in the previous module "The Bohr Model of Atom," Bohr assumed that the electrons can only orbit stably, without radiating, in certain orbits (named by Bohr as "stationary orbits"), at a certain discrete set of distances from the nucleus.
  • Given the energies of the lines in an atomic spectrum, it is possible (although sometimes very difficult) to determine the energy levels of an atom.
  • A theory of the atom or any other system must predict its energies based on the physics of the system.
  • This diagram is for the hydrogen-atom electrons, showing a transition between two orbits having energies $E_4$ and $E_2$.

• Multielectron Atoms

  • Atoms with more than one electron are referred to as multielectron atoms.
  • Atoms with more than one electron, such as Helium (He) and Nitrogen (N), are referred to as multielectron atoms.
  • Hydrogen is the only atom in the periodic table that has one electron in the orbitals under ground state.
  • The shielding theory also explains why valence shell electrons are more easily removed from the atom.
  • For example, consider a sodium cation, a fluorine anion, and a neutral neon atom.

• Energy of a Bohr Orbit

  • To be more general, we note that this analysis is valid for any single-electron atom.
  • So, if a nucleus has $Z$ protons ($Z=1$ for hydrogen, $Z=2$ for helium, etc.) and only one electron, that atom is called a hydrogen-like atom.
  • The tacit assumption here is that the nucleus is more massive than the stationary electron, and the electron orbits about it.
  • This is consistent with the planetary model of the atom.
  • This means that it takes energy to pull the orbiting electron away from the proton.

• Electric Charge in the Atom

  • Atoms contain negatively charged electrons and positively charged protons; the number of each determines the atom's net charge.
  • The number of protons in an atom defines the identity of the element (an atom with 1 proton is hydrogen, for example, and an atom with two protons is helium).
  • However, because electrons can be transferred from one atom to another, it is possible for atoms to become charged.
  • Atoms in such a state are known as ions.
  • Small electrons orbit the large and relatively fixed nucleus of protons and neutrons.

• Wave Nature of Matter Causes Quantization

  • This is the exact mechanism that causes quantization in atoms.
  • Assuming that an integral multiple of the electron's wavelength equals the circumference of the orbit, we have:
  • As previously discussed, Bohr was forced to hypothesize this as the rule for allowed orbits.
  • We now realize this as a condition for constructive interference of an electron in a (bound) circular orbit.
  • The third and fourth allowed circular orbits have three and four wavelengths, respectively, in their circumferences.