3s orbital

Spherically symmetric (radial) wave functions depend only on the radial distance r between the nucleus and the election. They are the Is, 2s, 3s. .. orbitals... 

The presenee of radial nodes also indieates that the eleetron has radial kinetie energy. The 3s orbital with 2 radial nodes has more radial kinetie energy than does the 3p whieh, in turn, has more than the 3d. On the other hand, the 3d orbital has the most angular energy... 

The third period begins with sodium and ends with argon The atomic number Z of sodium is 11 and so a sodium atom has 11 electrons The maximum number of electrons in the Is 2s and 2p orbitals is ten and so the eleventh electron of sodium occupies a 3s orbital The electron configuration of sodium IS 2s 2p 2p 2p is ... 

It is instructive to look at the form of the Is, 2s and 3s orbitals (Table 9.1). By convention, we use the dimensionless variable p = Zrjaa rather than r. Here 2 is the nuclear charge number and oq the first Bohr radius (approximately 52.9 pm). The quantity Z/n is usually called the orbital exponent, written These exponents have an increasing number of radial nodes, and they are orthonormal. 

The orbitals in an atom are organized into different layers, or electron shells, of successively larger size and energy. Different shells contain different numbers and kinds of orbitals, and each orbital within a shell can be occupied by two electrons. The first shell contains only a single s orbital, denoted Is, and thus holds only 2 electrons. The second shell contains one 2s orbital and three 2p orbitals and thus holds a total of 8 electrons. The third shell contains a 3s orbital, three 3p orbitals, and five 3d orbitals, for a total capacity of 18 electrons. These orbital groupings and their energy levels are shown in Figure 1.4. 

FIGURE 1.32 The radial distribution function tells us the probability density for finding an electron at a given radius summed over all directions. The graph shows the radial distribution function for the 1s-, 2s-, and 3s-orbitals in hydrogen. Note how the most probable radius icorresponding to the greatest maximum) increases as n increases. 

The plot with the most electron density closest to the origin (0, 0—the nucleus) arises from the s-orbital. Curve (b) corresponds to the 3s-orbital curve (a) corresponds to the 3p-orbital. 

The n orbitals on the two CO molecules interact with the same lobe of a vacant 3p orbital on a metal atom in the model for the acute angle coordination, and with different lobes for the obtuse angle coordination (Scheme 29b). Cychc orbital interaction occurs between the occupied 3s orbital and the vacant 3p orbitals on M and the n orbitals, n, and n, of the CO molecules (Scheme 29c). The phase is continuous for the same lobe interaction and discontinuous for the different lobe interaction (Scheme 29d, cf. Scheme 4). The acute-angle coordination is favored. 

An orbital is named by listing the numerical value for n, followed by the letter that corresponds to the numerical value for /. Thus, a 3s orbital has quantum numbers = 3,/ = 0.A5f orbital has n — 5, / — 3. Notice that the restrictions on / mean that many combinations of a and I do not correspond to orbitals that exist. For example, when n = I, / can only be zero. In other words, Is orbitals exist, but there are no Ip, Id, If, or Ig orbitals. Similarly, there are 2s and 2p orbitals but no 2d, 2f, or 2g orbitals. Remember that a restricts /, but / does not restrict a. Thus, a lOd orbital (a = 10, / = 2) is rather high in energy but perfectly legitimate, but there is no orbital with a = 2, / = 10. 

Dip the platinum loop in the solution and stick it in the flame. The result is a bright yellow glow. The color comes from two yellow emission lines that dominate the spectrum of sodium. The emission lines result from electrons dropping from the 3p to the 3s orbital. The two lines are very close to one another. The difference in energy is due to the slightly different energies of the electrons in the 3p orbital because of their spin. 

It must lose two electrons in its 3s orbital to obey the octet rule. This creates a magnesium ion with a charge of +2. Thus, a magnesium ion has the same electron configuration as the sodium ion but a different charge. Both ions have the same stable electron configuration as the noble gas neon ... 

Each atom in a bar of sodium has the same outer 3s orbital containing one electron. The individual atomic orbitals overlap, creating a huge number of molecular orbitals among which the electrons can move freely. This gives sodium and the other metals... 

However, the division of the electron density at the iron nucleus into contributions arising from Is through 4s contributions can be done conveniently at the level of the canonical molecular orbitals. This arises because the iron Is, 2s, and 3s orbitals fall into an orbital energy range where they are well isolated and hence do not mix with any hgand orbital. Hence, the Is, 2s, and 3s contributions are well defined in this way. The 4s contribution then arises typically from several, if not many, molecular orbitals in the valence region that have contributions from the iron s-orbitals. Thus, the difference between the total electron density at the nucleus and... 

To illustrate this point, the contributions of the occupied molecular orbitals to the total electron density at the nucleus are summarized in Table 5.2 for Fep4 (S - 5/2). It is evident from the table that the contributions coming from the orbitals at —6,966 eV must be assigned to the iron Is orbital, those from orbitals at —816 eV to the iron 2s orbital, and those from orbitals at —95 eV to the iron 3s orbital. In this highly symmetric complex, only two valence orbitals contribute to p(0), i.e. the —25 eV contribution from the totally symmetric ligand-group orbital that is derived from the F 2s orbitals and the —1 eV contribution from the totally symmetric... 

It is interesting to examine the probability of finding an electron as a function of distance when s orbitals having different n values are considered. Figure 2.6 shows the radial probability plots for the 2s and 3s orbitals. Note that the plot for the 2s orbital has one node (where the probability goes to 0)... 

FIGURE 11.2 Bands formed by interaction of orbitals on sodium atoms and their populations. The shaded bands are filled but the open bands are empty. The band arising from the 3s orbitals is only half filled because there is only one electron per atom in the 3s state. 

Because there is one 3s orbital per Na atom, and since the number of energy levels (molecular orbitals) created is equal to the number of atomic orbitals initially present, there are 7.02 x 1020 energy levels present in the conduction band of this sample. Also, there is one 3s electron contributed by each Na atom, for a total of 7.02 x 1020 electrons. Because each energy level can hold two electrons, the conduction band is half full. 

The Na atom has one half-filled (3s1) and three empty orbitals (3px, 3py, 3pz). The number of valence orbitals is greater than the number of valence electrons. In the solid state, sodium atoms are surrounded by other sodium atoms. Thus, the valence electron of the sodium atom in the 3s orbital can move to the empty orbitals (3px, 3py, 3pz) of neighbouring atoms. When each sodium valence electron behaves in this way a sea of electrons is built up around the sodium atoms (now positive ions, having lost a valence electron). 

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