Helium orbital diagram

Arrows are added to an orbital diagram to show the distribution of electrons in the possible orbitals and the relative spin of each electron. The following is an orbital diagram for a helium atom. 

A helium atom, for example, has two electrons. The electron configuration and orbital diagram for helium are ... 

The upward arrow denotes one of the two possible spins (one of the two possible m, values) of the electron in the hydrogen atom (the other possible spin is indicated with a downward arrow). Under certain circumstances, as we will see shortly, it is useful to indicate the explicit locations of electrons. The orbital diagram for a helium atom in the ground state is... 

After helium, the next element in the periodic table is lithium, which has three electrons. Because of the restrictions imposed by the Pauli exclusion principle, an orbital can accommodate no more than two electrons. Thus, the third electron cannot reside in the Ij orbital. Instead, it must reside in the next available orbital with the lowest possible energy. According to Figure 6.23, this is the 2s orbital. Therefore, the electron configuration of lithium is l5 25 and the orbital diagram is... 

We will draw orbital diagrams and write electron configurations for the elements H and He in Period 1. The H orbital (which is the 1 sublevel) is written first because it has the lowest energy. Hydrogen has one electron in the 1 sublevel helium has two. In the orbital diagram, the electrons for helium are shown as arrows pointing in opposite directions. 

Since two electrons occupying the same orbital have three identical quantum numbers (n, I, and mi), they must have different spin quantum numbers. Since there are only two possible spin quantum numbers (-1-5 and -5), the Pauli exclusion principle implies that each orbital can have a maximum of only two electrons, with opposing spins. By applying the exclusion principle, we can write an electron configuration and orbital diagram for helium as follows ... 

The Grotrian diagram in Figure 7.9 gives the energy levels for all the terms arising from the promotion of one electron in helium to an excited orbital. 

Figure 7.9 Grotrian diagram for helium. The scale is too small to show splittings due to spin-orbit coupling...

If we imagine the nuclei to be forced together to = 0, the wave function Is A + Iss will approach, as a limit, a charge distribution around the united atom that has neither radial nor angular nodal planes. This limiting charge distribution has the same symmetry as the Is orbital on the united atom, Helium. On the other hand, the combination Isa Iss has a nodal plane perpendicular to the molecular axis at all intemuclear separations. Hence its limit in the united atom has the symmetry properties of a 2p orbital. A simple correlation diagram for this case is ... 

Fig. 1 shows the level diagram of antiprotonic helium which was experimentally established by observing several laser-induced transitions of the antiproton (see talk by T. Yamazaki [4]). Each level in Fig. 1 is split due to the presence of three angular momenta the orbital angular momentum L (mainly carried by the p), and the spins of the electron Se and the antiproton Sp. These momenta couple according to the following scheme ...

The helium atom has two electrons and they can both fit into the Is orbital providing they have opposite spins. The other change to the diagram is that, with two electrons and electron repulsion a factor, the 2s orbital is now lower in energy than the three 2p orbitals, though these three are still degenerate. 

We will now apply the MO model to the helium molecule (He2). Does this model predict that this molecule is stable Since the He atom has a Is2 configuration, Is orbitals are used to construct the MOs. Therefore the molecules will have four electrons. From the diagram shown in Fig. 14.29, it is apparent that two electrons are raised in energy and two are lowered in energy. Thus the bond order is zero ... 

Figure 2.6 The left side shows the orbital interaction diagram for two hydrogen atoms and the right side shows the interaction of two helium atoms (see molecular orbitals drawn in Fig. 1.6).

The arrow represents an electron spinning in a particular direction. The next element is helium, Z = 2. It has two protons in its nucleus and so has two electrons. Because the Is orbital is the most desirable, both electrons go there but with opposite spins. For helium, the electron configuration and box diagram are... 

Figure 5.7 Application of the general spreadsheet to the calculation of the energy of the helium atom using the Pople, Hehre and Stewart sto-6g) basis set of Table 1.6 and the best Slater exponent, also reported elsewhere (8,9) from variation of the entry in cell oneel D l. For the Slater-rules exponent, 1.7, the helium energy is found to be —2.8461945 hartree with the Is orbital energy equal to —0.8918763 H. Note, the detail shown for the Vijkl term. On this spreadsheet all 1296 [6 integrals] are calculated, with the degeneracies over the primitives, colour-coded in the second diagram in the figure.

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