Beryllium atomic energy levels

From Figure 6.8 it is possible to predict the electron configurations of atoms of elements with atomic numbers 1 through 36. Because an s sublevel can hold only two electrons, the Is is filled at helium (Is2). With lithium (Z = 3), the third electron has to enter a new sublevel This is the 2s, the lowest sublevel of the second principal energy level. Lithium has one electron in this sublevel (ls s1)- With beryllium (Z = 4), the 2s sublevel is filled (ls22s2). The next six elements fill the 2p sublevel. Their electron configurations are... 

We describe in this Subsection the application of local-scaling transformations to the calculation of the energy for the lithium and beryllium atoms at the Hartree-Fock level [113]. (For other reformulations of the Hartree-Fock problem see [114] and referenres therein.) The procedure described here involves three parts. The first part is orbital transformation already discussed in Sect. 2.5. The second is intra-orbit optimization described in Sect. 4.3 and the third is inter-orbit optimization discussed in Sect. 4.6. 

Fig. 2-14.—Energy-level diagram for the neutral beryllium atom.

Eight electrons from two beryllium atoms fill the four lowest energy levels, itXk, o s, 2j °zx- yielding a net bond order of zero, as in He, with an electron configuration of ... 

There are exceptions to the octet rule. Helium, for example, is incredibly stable with just two valence electrons in its outermost principal energy level. The same holds true for lithium and beryllium as well. This indicates that it isn t so much having an octet that stabilizes the atom, as it is the issue of having a full outermost principal energy level. 

Each of the two sp-hybrid orbitals contains a single unpaired electron which is readily shared with a similar electron on another atom such as hydrogen. Notice how the sp hybrid orbital is intermediate in energy between the 2s and 2p orbitals of atomic beryllium. This means that it doesn t cost the beryllium atom much in energy to get its two outer electrons into the sp hybrid- what the beryllium atom must pay in order to promote its 2s electron up to the level of the sp hybrid, the atom more than gains in the energy lost when the previously promoted 2p electron now drops down to the sp-hybrid level. 

Back to the Periodic Table. In the second row, we start with lithium. It has a completely filled If energy level, plus an extra electron that hangs out in the 2s energy level. With an open slot in that energy level, lithium readily interacts with other atoms. The next atom in the second row is beryllium, which has... 

The key to solving this type of problem is to look at the electron configuration of the element. Beryllium, with an atomic number of 4, has 4 electrons, giving it an electron configuration of Is2 2s2. The nucleus and the two electrons in the first energy level (Is2) make up the kernel of the atom, and they are represented by the elemental symbol in our Lewis dot notation. The two electrons in the second energy level (2s2) represent the valence electrons, which are represented by dots in the Lewis dot notation. So, to construct the proper notation, we write the elemental symbol and two dots to the left of the symbol, as shown here. 

El.30 Frontier orbitals of Be Recall from Section 1.9(c) Electron affinity, that the frontier orbitals are the highest occupied and the lowest unoccupied orbitals of a chemical species (atom, molecule, or ion). Since the ground-state electron configuration of a beryllium atom is ls 2s , the frontier orbitals are the 2s orbital (highest occupied) and three 2p orbitals (lowest unoccupied). Note that there can be more than two frontier orbitals if either the highest occupied and/or lowest unoccupied energy levels are degenerate. In the case of beryllium we have four frontier orbitals (one 2s and three 2p). 

Calculation of the energy and wavefunction for the beryllium atom at the Hartree-Fock level by in the context of local-scaling transformations... 

In a lithium atom the Is orbital, close to the nucleus, is occupied by two electrons, while the 2s orbital, further from the nucleus, contains one. In beryllium, there is a second electron in the 2s orbital. As before the energy levels will change as the nuclear charge increases, so the orbital occupancy in Li and Be can be represented as shown below. 

This is why we took the beryllium atom and not just the helium atom, in which the energy difference between the orbital levels Is and 2s is much larger (i.e., the correlation energy much smaller). 

Figure 5.3 illustrates a beryllium atom with its energy levels. The atom is composed of 4 protons and 5 neutrons in the nucleus, and 4 electrons arranged in 2 shells (or orbital layers) outside the nucleus. The first shell contains 2 electrons and the second shell contains 2 electrons. 

The increase to 900 kJ mol" in the case of the beryllium atom is due to the increase in effective nuclear charge, offset by interelectronic repulsion of the two 2s electrons. The electron most easily removed is one of the pair in the 2s orbital. In the case of the boron atom, in spite of an increase in nuclear charge there is a decrease in the first ionization energy to 799 kJ mol. This is because the electron removed is from a 2p orbital, which is higher in energy than the 2s level. 

On the other hand, as we move across a period from left to right, additional electrons are being added to the same energy level, i.e., the value of n does not change. Look at the second period of elements, lithium to neon. An atom of lithium has three protons in its nucleus, beryllium has four protons, boron has five protons, and so forth until we reach neon with ten protons in its nucleus. All the protons have positive charges. As we increase the positive charge on the nucleus, the total electrostatic force on all the electrons increases. All of the electrons are pulled a little closer to the nucleus. Therefore, as the charges on the nuclei increase, the atoms become a little smaller in size. 

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