![]() The Z eff for a 3 p electron, on the other hand, is Z eff = 17 – 10 = 7 because there are 10 electrons shielding the 3 p electron (2 electrons in n = 1 and a total of 8 electrons in n = 2). Therefore, Z eff = 17 – 2 = 15 for a 2s electron of Cl. The only electrons that will shield a 2 s electron are the 1 s electrons, and there are two of them. For Cl, Z = 17 and the electron configuration is 1 s 22 s 22 p 63 s 23 p 5. For example, consider a 2 s electron of Cl. Note that while we often refer to the Z eff of a valence electron, we can calculate the Z eff for any electron by taking into account only the number of core electrons that are shielding. Remember from a previous chapter, Z is the number of protons in the nucleus. There are more exact ways of determining Z effwhich include the shielding contribution of electrons in the same shell, but the approximate formula we use in this course is accurate enough to be very useful. In this class, we will calculate Z eff = Z – S, where S is the number of core electrons that are shielding the valence electrons. Thus, Z eff for valence electrons increases as we move from left to right across a period. But, there is only a small probability of the 2 s electron (electron in the same valence shell) to shield the 2p electron of interest. Thus, each time we move from one element to the next across a period, Z increases by one, but the shielding increases only slightly. In Figure 1B, if a 2 p electron exists at a distance r 1, most likely the 1 s electrons (core electrons) will be between the electron of interest and the nucleus. Core electrons are adept at shielding, while electrons in the same valence shell do not block the nuclear attraction experienced by each other as efficiently. Shielding is determined by the probability of another electron being between the electron of interest and the nucleus, as well as by the electron–electron repulsions the electron of interest encounters. Only electrons that are likely to be found between the electron of interest and the nucleus contribute to shielding. distance from the nucleus shows that electrons in the 1 s orbital are more likely to be found closer to the nucleus than electrons in the 2 s or 2 p orbitals. Electrons further from the nucleus (red) do not affect the Z eff between the electron of interest and the nucleus. (A) The interior electron cloud (light blue) shields the outer electron of interest from the full attractive force of the nucleus. The Z eff experienced by an electron in a given orbital depends not only on the spatial distribution of the electron in that orbital but also on the distribution of all the other electrons present. ![]() Consequently, the Z eff is always less than the actual nuclear charge, Z. An effective nuclear charge is t he nuclear charge an electron actually experiences because of shielding from other electrons closer to the nucleus ( Figure 1). As a result, the electron farther away experiences an effective nuclear charge ( Z eff). Hence these electrons will cancel a portion of the positive charge of the nucleus and thereby decrease the attractive interaction between the nucleus and the electron farther away. If an electron is far from the nucleus (i.e., if the distance r between the nucleus and the electron is large), then at any given moment, most of the other electrons will be between that electron and the nucleus. There are no known solutions to the Schrodinger equation for this problem, so one must use approximate methods to find the orbitals and their energies. In addition there are attractive interactions between each of the two electrons with the nucleus. From Coloumb’s law we know that there is a repulsive interaction that depends on the distance between them. For example, in helium there are two electrons. When more than one electron is present, however, the total energy of the atom or the ion depends not only on attractive electron-nucleus interactions but also on repulsive electron-electron interactions. ![]() | Key Concepts and Summary | Key Equations | Glossary | End of Section Exercises | Effective Nuclear Charge (Z eff)įor an atom or an ion with only a single electron, we can calculate the potential energy of an electron by considering only the electrostatic attraction between the positively charged nucleus and the negatively charged electron. | Effective Nuclear Charge (Z eff) | Shielding | Variation in Atomic Radius | Correlate the effective nuclear charge with selected trends in periodic properties.
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