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Answer on the question #54596 – Chemistry – General chemistry Question: What is meant by effective nuclear charge? What are the factors that determine the effective nuclear charge? How is it calculated? Answer: It is the net positive charge experienced by an electron in a multi-electron atom. The term "effective" is used because the shielding effect of negatively charged electrons prevents higher orbital electrons from experiencing the full nuclear charge by the repelling effect of inner-layer electrons. The effective nuclear charge experienced by the outer shell electron is also called the core charge. It is possible to determine the strength of the nuclear charge by the oxidation number of the atom. Calculation: In an atom with one electron, that electron experiences the full charge of the positive nucleus. In this case, the effective nuclear charge can be calculated from Coulomb's law. However, in an atom with many electrons the outer electrons are simultaneously attracted to the positive nucleus and repelled by the negatively charged electrons. The effective nuclear charge on such an electron is given by the following equation: where Z is the number of protons in the nucleus (atomic number), and S is the average number of electrons between the nucleus and the electron in question (the number of nonvalence electrons). S can be found by the systematic application of various rule sets, the simplest of which is known as "Slater's rules" (named after John C. Slater). Douglas Hartree defined the effective Z of a Hartree–Fock orbital to be: where is the mean radius of the orbital for hydrogen, and is the mean radius of the orbital for an electron configuration with nuclear charge Z. www.AssignmentExpert.com .

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1.1 Effective Nuclear Charge 1.2 Effective Nuclear Charge 1.3
Periodic Trends Periodic Trends 1.1 Effective Nuclear Charge 1.2 Effective Nuclear Charge The interaction between the nuclear charge and the Zeff = nuclear charge actually experienced by an valence electrons (how many? how far away?) is electron critical Simplest approximation The nuclear charge experienced by the valence Zeff = Z - # core electrons electrons (Zeff ) impacts how tightly the valence electrons are held Assumption How tightly the valence electrons are held influences atomic size, ionization energy, electron affinity, and Examples reactivity Periodic Trends Periodic Trends 1.3 Effective Nuclear Charge 1.4 Slater’s Rules Slater’s rules acknowledge the imperfect shielding Slater’s rules assume imperfect shielding caused by orbital penetration Zeff = Z – where is calculated using Slater’s rules 1. GthbitlidGroup the orbitals in order: (1s) (2s,2p) (3s,3p) (3d) (4s,4p) (4d) (4f) (5s,5p)… 2. To determine , sum up the following contributions for the electron of interest: a. 0 (zero) for all electrons in groups outside (to the right of) the one being considered b. 0.35 for each of the other electrons in the same ggp(proup (except for 1s group where 0.30 is used) c. If the electron is in a (ns,np) group, 0.85 for each electron in the next innermost (to the left) group d. If the electron is in a (nd) or (nf) group, 1.00 for each electron in the next innermost (to the left) group e. 1.00 for each electron in the still lower (farther in) groups 1 Periodic Trends Periodic Trends 1.5 Using Slater’s Rules 1.6 Using Slater’s Rules What do the 1.0, 0.85 and 0.35 factors mean? Fluorine’s Zeff calculated using the simple approximation = 7 and using Slater’s rules = 5.20.
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Important Factoids in Understanding Effective Nuclear Charge
CHEM 1B Important Factoids in Understanding Effective Nuclear Charge To understand the concept of effective nuclear charge, we focus on one electron (usually a valence or outer electron) and consider the forces the other charged particles exert on this electron. In an atom with more than one electron, each electron will ‘feel’ both attractive forces from the positive nucleus and repulsive forces from the other electrons. Qualitatively, Zeff is the NET (or effective) ATTRACTIVE charge that the electron ‘feels’, taking into account both the attractive and repulsive forces. The attractive part of Zeff is just Z, the positive charge on the nucleus ‘pulling’ on the electron (i.e. the atomic number) The repulsive part, repulsion from the other electrons, is referred to as ‘shielding’. It gets this designation because an electron is ‘shielded’ from the pull of the positive nucleus by the repulsion of the other electrons. To provide shielding an electron must have its probability density closer to the nucleus than the outer electron (and thus partially neutralize the + nuclear charge). Thus Zeffective=+Z ‐(shielding of other electrons) [note the + sign for the attractive part and –sign for the repulsive part] MORE SHIELDING ï LOWER Zeff LESS SHIELDING ï HIGHER Zeff In terms of Zeff and the principal quantum number n of the outer electron, the ionization energy and size of an atom can be approximated as: 22 2 18ZZeff 18 eff 11 n EnZeff, 2.18 10 J22 and IE 2.18 10 J and ravg 5.28 10 m nn Zeff An approximate Zeff can be obtained empirically from experimental ionization energies: 12 nIE2 experimental Zeff 18 2.18 10 J The lecture will discuss: For 1‐electron atoms or ions [H, He+, Li2+, Be3+, etc.] there is no shielding and Zeff∫Z [Z=+1, +2, +3, +4, etc.] For He 1s2 the second electron (in the same 1s shell) provides 0.66 shielding [reduces the pull of the nucleus from Z= +2 to Zeffº1.34] For Li 1s22s each of the two 1s electrons provides 0.84 shielding for the outer 2s electron [the two reduce the pull of the nucleus from Z=+3 to Zeffº3‐2ä0.87=1.26.
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Lanthanides.Pdf
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362 Leture 6
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I Anomalous Properties of Elements I That MOW "Long Periods" of Elements
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