Atomic Orbitals Penetration Effects

The atom is the smallest unit of a substance that has its chemical properties. From the 118 known elements, only 92 are found in nature. The other elements have been obtained artificially and have generally a very short life, with a rapid decay. 

The atomic model shows that the atom is made of three fundamental particles protons, neutrons, and electrons. The protons and neutrons are found in the center of the atom forming a dense, positively charged nucleus. The protons have the electric charge +1 and the weight equal to one atomic mass unit. The neutrons have a weight equal to one atomic mass unit too, but do not have electric charge. 

The protons, neutrons, and electrons are always written in lowercase p, n, and e. The uppercase versions of these letters are not being used since they have other meanings in both chemistry and physics (for example, P is phosphorus and E is energy). 

The nucleus of any atom or element is characterized by an atomic number, Z, equal to the number of protons and a mass number. A, equal to the total number of protons and neutrons (A=Z+n). 

The electrons surround the nucleus like clouds, spinning at high speeds on then-paths called orbitals. They have the same electrical charge as protons, but have the opposite sign, namely negative. 

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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 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. 

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 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. 

Consider the suggestion that the ls 2s excited state of helium is lower in energy than the ls 2p excited state because the 2s orbital penetrates the Is core electron density more effectively, thereby seeing greater stabilization nearer the nucleus. Let s estimate that stabilization by calculating an r-dependent effective atomic number Z g r) equal to the... 

FIGURE 12.5 Plots of 47rF Pp for the 3d and 4s wavefunctions. Note that the plots have the same x-axis, and that the 4s electron has some probability of being rather close to the nucleus. For multielectron atoms, the penetration of the 4s electron combined with the shielding effect of the other electrons serves to make the 4s orbital the next one occupied by electrons, rather than the 3d. 

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