Orbital penetration effects

The treatment of atoms with more than one electron (polyelectronic atoms) requires consideration of the effects of interelectronic repulsion, orbital penetration towards the nucleus, nuclear shielding, and an extra quantum number (the spin quantum number) which specifies the intrinsic energy of the electron in any orbital. The restriction on numbers of atomic orbitals and the number of electrons that they can contain leads to a discussion of the Pauli exclusion principle, Hund s rules and the aufbau principle. All these considerations are necessary to allow the construction of the modern form of the periodic classification of the elements. 

The penetration effect also helps to explain why the 4s orbital fills before the 3d orbital. Recall that potassium has the electron configuration ls22s22p63s23p64s1 rather than the expected ls22s22p63s23p63d1. We can explain this result by observing that an electron in a 4s orbital penetrates much... 

The radial distribution of electron probability density for the sodium atom. The shaded area represents the 10 core electrons. The radial distributions of the 3s, Ip, and 3d orbitals are also shown. Note the difference in the penetration effects of an electron in these thiee orbitals. 

The Orbital Penetration Term in Aromatic Substitutuent Effects. 

What is penetration How is it related to shielding Use the penetration effect to explain the difference in relative orbital energies of a 3p and a 3d electron in the same atom. 

The ( -f 1)5 orbitals always fill before the nd orbitals. For example, the 5s orbitals fill in rubidium and strontium before the 4<7 orbitals fill in the second row of transition metals (yttrium through cadmium). This early filling of the 5 orbitals can be explained by the penetration effect. For example, the 4s orbital allows for so much more penetration to the vicinity of the nucleus that it becomes lower in energy than the 3d orbital. Thus the 4s fills before the 3d. The same things can be said about the 5s and 4d, the 65 and 5d, and the Is and 6d orbitals. 

Orbital penetration is a term that illustrates the proximity of electrons in an orbital to the nucleus. If the penetration for an electron is greater, it experiences less shielding, and therefore a larger effective nuclear charge. 

The penetration effect also helps to explain why the 4s orbital fills before the 3d orbital. Recall that potassium has the electron confignration ls 2s 2p 3s 3p 4s rather than the expected ls 2s 2p 3s 3p 3r/. We can explain this result by observing that an electron in a 4s orbital penetrates mnch more than an electron in a 3d orbital, as shown graphically in Fig. 12.34. Note that although the most probable distance from the nnclens for a 3d electron is less than that for a 4s electron, the 4s electron has a significant probability of penetrating close to the nucleus. This explains why the potassinm atom in its lowest-energy state has its last electron in the 4s orbital rather than in the 3d orbital. 

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