Stable orbits

For elements adjacent to the noble gases the principal orbitals used in bond formation are those formed by hybridisation of the s and p orbitals. For the transition elements there are nine stable orbitals to be taken into consideration, which in general are hybrids of five d orbitals, one s orbital, and three p orbitals. An especially important set of six bond orbitals, directed toward the comers of a regular octahedron, are the d2sps orbitals, which are involved in most of the Werner octahedral complexes formed by the transition elements. 

With the development of the quantum-mechanical theory of valence it was recognized5 that a hydrogen atom, with only one stable orbital, cannot form more than one pure covalent bond6 and that the attraction... 

The higher the value of the 1 quantum number, the more that orbital is screened by electrons in smaller, more stable orbitals. 

The chemical behavior of an atom is determined by the electrons that are accessible to an approaching chemical reagent. Accessibility, in turn, has a spatial component and an energetic component. An electron is accessible spatially when it occupies one of the largest orbitals of the atom. Electrons on the perimeter of the atom, farthest from the nucleus, are the first ones encountered by an incoming chemical reagent. An electron is accessible energetically when it occupies one of the least stable occupied orbitals of the atom. Electrons in less stable orbitals are more chemically active than electrons in more stable orbitals. 

A neutral helium atom has two electrons. To write the ground-state electron configuration of He, we apply the aufbau principle. One unique set of quantum numbers is assigned to each electron, moving from the most stable orbital upward until all electrons have been assigned. The most stable orbital is always ly( = l,/ = 0, JW/ = 0 ). 

Aluminum has Z= 13, so a neutral atom of A1 has 13 electrons. Place the 13 electrons sequentially, using arrows, into the most stable orbitals available. Two electrons fill the = 1 orbital, eight electrons fill the = 2 orbitals, two electrons fill the 3. S orbital, and one electron goes in a 3 orbital. 

When an atom absorbs a photon, the gain in energy promotes an electron to a less stable orbital. As electrons move into less stable orbitals, they have less electrical attraction for the nucleus. If the absorbed photon has enough energy, an electron can be ejected from the atom, as occurs in photoelectron spectroscopy. 

The minimum amount of energy needed to remove an electron from a neutral atom is the first ionization energy ij E ). Variations in ionization energy mirror variations in orbital stability, because an electron in a less stable orbital is easier to remove than one in a more stable orbital. 

The aufbau principle must be obeyed when an electron is added to a neutral atom, so the electron goes into the most stable orbital available. Hence, we expect trends in electron affinity to parallel trends in orbital stability. However, electron-electron repulsion and screening are more important for negative ions than for neutral atoms, so there is no clear trend in electron affinities as ft increases. Thus, there is only one general pattern ... 

The electrons in molecules obey the aufbau principle, meaning that they occupy the most stable orbitals available to them. 

Figure 20-12 summarizes the electrical interactions of an octahedral complex ion. The three orbitals that are more stable are called 2 g orbitals, and the two less stable orbitals are called Sg orbitals. The difference in energy between the two sets is known as the crystal field splitting energy, symbolized by the Greek letter h. 

The ions introduced into the trap are maintained on stable orbits applying DC and RF potential to the electrodes. To separate ions, according to their m/z, a RF scan is made. While the RF amplitude increases, ions with higher m/z values are destabilized and they leave the ion trap moving towards the detector. 

This accounts for the fact that the line spectrum of hydrogen shows only lines having certain wavelengths. In order for the electron to move in a stable orbit, the electrostatic attraction between it and the proton must be balanced by the centrifugal force that results from its circular motion. As shown in Figure 1.7, the forces are actually in opposite directions, so we equate only the magnitudes of the... 

De Broglie s work clearly shows that a moving electron can be considered as a wave. If it behaves in that way, a stable orbit in a hydrogen atom must contain a whole number of wavelengths, or otherwise there would be interference that would lead to cancellation (destructive interference). This condition can be expressed as... 

This experiment established the nuclear model of the atom. A key point derived from this is that the electrons circling the nucleus are in fixed stable orbits, just like the planets around the sun. Furthermore, each orbital or shell contains a fixed number of electrons additional electrons are added to the next stable orbital above that which is full. This stable orbital model is a departure from classical electromagnetic theory (which predicts unstable orbitals, in which the electrons spiral into the nucleus and are destroyed), and can only be explained by quantum theory. The fixed numbers for each orbital were determined to be two in the first level, eight in the second level, eight in the third level (but extendible to 18) and so on. Using this simple model, chemists derived the systematic structure of the Periodic Table (see Appendix 5), and began to... 

We are all familiar with forces between bodies on a macroscopic scale. If one sits at their desk on earth pondering the view and inadvertently lets go of their lunch sandwich it falls until it lands on your manuscript, your lap or the floor—right Better yet, a cannonball and a softball fall at the same rate. It is the definition of gravity . Long after the Tower of Pisa experiments, we discovered why the moon is in seemingly stable orbit around the earth and the earth around the sun is related to forces between bodies. We are also familiar with electrostatic forces and their effects. Dust from the air in the room is attracted to the screen of everyone s TV because of the electrostatic charge it develops. It would seem reasonable that attraction occurs on a smaller scale and even on a molecular scale that does not involve energies on the order of true chemical bonds. 

The simplest exciton can be modeled by a hydrogen atom, with the electron and hole (equivalent to the hydrogen nucleus) in a stable orbit around each other. Within this model, two basic types of excitons can occur in crystalline materials ... 

In simple English, this implies that if you were in a 4-D universe and launched planets toward a sun, the planets would either fly away to infinity or spiral into the sun. (This is in contrast to a (3 + 1) universe that obviously can, for example, have stable orbits of moons around planets.) A similar problem occurs in quantum mechanics, in which a study of the Schrodinger equation shows that the hydrogen atom has no bound states for n > 5. This seems to suggest that it is difficult for higher universes to be stable over time and contain creatures that can make observations about the universe. 

Let us first discuss the helium atom. The most stable orbital in the helium atom is the Is orbital, with n 1, l = 0, = 0. There are... 

Fig. 2-15.—The approximate sequence of energy values for atomic orbitals, the lowest circle representing the most stable orbital (Is). Each circle represents one atomic orbital, which can be ocoupied either by one electron or by two electrons with opposed spins.

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