The formula for calculating the energies of an electron in a hydrogenlike ion is given in the following equation. En = - n = 1, 2, 3,... This equation cannot be applied to many-electron atoms. One way to modify it for the more complex atoms is to replace Z with (Z - ơ), where Z is the atomic number and ơ is a positive dimensionless quantity called the shielding constant. The physical significance of o is that it represents the extent of shielding that the inner electrons exert on each other. Thus, the quantity (Z - o) is appropriately called the effective nuclear charge. Calculate the value of o if the first ionization energy of oxygen is 2.18x10-18 ) per atom. (In your calculations, ignore the minus sign in the given equation.) 10

The formula for calculating the energies of an electron in a hydrogenlike ion is given in the following equation. En = - n = 1, 2, 3,... This equation cannot be applied to many-electron atoms. One way to modify it for the more complex atoms is to replace Z with (Z - ơ), where Z is the atomic number and ơ is a positive dimensionless quantity called the shielding constant. The physical significance of o is that it represents the extent of shielding that the inner electrons exert on each other. Thus, the quantity (Z - o) is appropriately called the effective nuclear charge. Calculate the value of o if the first ionization energy of oxygen is 2.18x10-18 ) per atom. (In your calculations, ignore the minus sign in the given equation.) 10

Introductory Chemistry: An Active Learning Approach

6th Edition

ISBN:9781305079250

Author:Mark S. Cracolice, Ed Peters

Publisher:Mark S. Cracolice, Ed Peters

Chapter11: Atomic Theory :the Quantum Model Of The Atom

Section: Chapter Questions

Problem 109E

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The energy of any one-electron species in its nth state (n=principalquantumnumber) is given by E=BZ2/ n2, where Z is the charge on the nucleus and B is 2.1801018J. Find the ionization energy of the Li2+ ion in its first excited state in kilojoules per mole.
Palladium, with an electron configuration of [Kr] 4d10, is an exception to the aufbau principle. Write the electron configuration of the 2+ cation of palladium. Does the fact that palladium is an exception influence the electron configuration of Pd2+?
Write condensed electron configurations for the following atoms and ions, using appropriate noble-gas core abbreviations. Put superscripted electron count numbers in parentheses. Examples: Fe = [Ar]4s(2)3d(6), Sn²+ = [Kr]4d(10)5s(2), s2- = [Ar]. (a) Te2- (b) I = (c) Fe3+ (d) v3+ (e) Ba2+ =
(ii) How would you expect the second ionization energies for Na and Mg to compare? Explain using both a qualitative and quantitative (Slater’s rules) argument. (iii) Does your answer for (ii) correspond to what you know about the common ions formed by Na and Mg? Explain.
(a) Write the electron configuration for Li and estimate theeffective nuclear charge experienced by the valence electron.(b) The energy of an electron in a one-electron atom or ion equals (-2.18 x 10-18 J) aZ2/n2 b, where Z is the nuclear chargeand n is the principal quantum number of the electron. Estimatethe first ionization energy of Li. (c) Compare the resultof your calculation with the value reported in Table 7.4 andexplain the difference. (d) What value of the effective nuclearcharge gives the proper value for the ionization energy? Doesthis agree with your explanation in part (c)?
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