Effective Nuclear Charge - Student Notes PDF

Learning objective - 2 ✓ Understand and explain the concept of effective nuclear charge 1  2 EFFECTIVE NUCLEAR CHARGE Many properties of atoms depend on electron configuration and on how strongly the outer electrons in th...

Learning objective - 2 ✓ Understand and explain the concept of effective nuclear charge 1  2 EFFECTIVE NUCLEAR CHARGE Many properties of atoms depend on electron configuration and on how strongly the outer electrons in the atoms are attracted to the nucleus. Coulomb’s law tells us that the strength of the interaction between two electrical charges depends on the magnitudes of the charges and on the distance between them. Thus, the attractive force between an electron and the nucleus depends on: ✓ the magnitude of the nuclear charge ✓ the average distance between the nucleus and the electron The force increases as the nuclear charge increases and decreases as the electron moves farther from the nucleus. 2  In a many-electron atom, each electron is simultaneously attracted to the nucleus and repelled by the other electrons. In general, there are so many electron–electron repulsions that we cannot analyze the situation exactly. We can, however, estimate the attractive force between any one electron and the nucleus by considering how the electron interacts with the average environment created by the nucleus and the other electrons in the atom. We treat each electron as though it were moving in the net electric field created by the nucleus and the electron density of the other electrons. We view this net electric field as if it results from a single positive charge located at the nucleus, called the effective nuclear charge, Zeff. The effective nuclear charge acting on an electron in an atom is smaller than the actual nuclear charge (Zeff < Z ) because the effective nuclear charge includes the effect of the other electrons in the atom. 3  In any many-electron atom, the inner electrons partially screen outer electrons from the attraction of the nucleus, and the relationship between Zeff and the number of protons in the nucleus Z is Zeff = Z – S ; Equation 7.1 where S is a positive number called the screening constant. s is inner electron inner electron is selain valence It represents the portion of the nuclear charge that is screened from a valence electron by the other electrons in the atom. Because core electrons are most effective at screening a valence electron from the nucleus, the value of S is usually close to the number of core electrons in an atom. 4 Effective nuclear charge & repulsive effect of electrons Thus, effective nuclear charge (Zeff) is the nuclear charge felt by an electron when both the actual nuclear charge (Z) and the repulsive effects (shielding) of the other electrons are taken into account. Repulsive or “shielding” effect refers to a decrease in attraction between the nucleus and electrons in an atom. This repulsive effect causes by mutual repulsion of electrons. lagi banyak shell, lagi besar shielding effect 5  Let’s look at the Na atom to see what to expect for the magnitude of Zeff. Sodium has the electron configuration [Ne]3s1. The nuclear charge is 11+, and there are 10 core electrons (1s2 2s2 2p6 ). We therefore expect S to equal 10 and the 3s electron to experience an effective nuclear charge of Zeff = 11 – 10 = 1+ (FIGURE 7.2). The situation is more complicated, however, because the 3s electron has a small probability of being closer to the nucleus, in the region occupied by the core electrons. Thus, there is a probability that this electron experiences a greater attraction than our simple S = 10 model suggests. This greater attraction turns out to increase the value of Zeff for the 3s electron in Na from our expected Zeff = 1+ to Zeff = 3+. In other words, the fact that the 3s electron spends some small amount of time close to the nucleus changes the value of S in Equation 7.1 from 10+ to 8.5+. 6  The notion of effective nuclear charge also explains an important effect we noted in “Atomic Structure” chapter. For a many-electron atom, the energies of orbitals with the same n value increase with increasing l value. For example, in the carbon atom, electron configuration 1s2 2s2 2p2, the energy of the 2p orbital (l = 1) is higher than that of the 2s orbital (l = 0) even though both orbitals are in the n = 2 shell. This difference in energies is due to the radial probability functions for the orbitals (FIGURE 7.3). The greater attraction between the 2s electron and the nucleus leads to a lower energy for the 2s orbital than for the 2p orbital. The same reasoning explains the general trend in orbital energies (ns < np < nd) in many-electron atoms. 7  3Li Finally, let’s examine trends in valence-electron Zeff values. The effective nuclear charge increases from left to right across any period of the periodic table. Although the number of core electrons stays the same across the period, the number of protons increases. The valence electrons added to counterbalance the increasing nuclear charge screen one another ineffectively. Thus, Zeff increases steadily. For example, the core electrons of lithium (1s2 2s1) screen the 2s valence electron from the 3+ nucleus fairly efficiently. 4Be Consequently, the valence electron experiences an effective nuclear charge, Zeff of roughly 3 – 2 = 1+. For beryllium (1s2 2s2 ) the effective nuclear charge experienced by each valence electron is larger because here the 1s electrons screen a 4+ nucleus, and each 2s electron only partially screens the other. Consequently, the effective nuclear charge experienced by each 2s electron is about 4-2 = 2+. 8  group Going down a column, the effective nuclear charge experienced by valence electrons changes far less than it does across a period. For example, we would expect the effective nuclear charge experienced by the valence electrons in lithium and sodium to be about the same, roughly 3 – 2 = 1+ for lithium and 11 – 10 = 1+ for sodium. In fact, however, effective nuclear charge increases slightly as we go down a column because the more diffuse core electron cloud is less able to screen the valence electrons from the nuclear charge. In the case of the alkali metals, Zeff increases from 1.3+ for lithium, to 2.5+ for sodium, to 3.5+ for potassium. Remember that this formula Zeff = Z – S; is only use to estimate the value of Zeff, although the actual value of Zeff might be slightly different. 9 Ne 2s 2p ? Na 3s 3p 10