A hyavogen-ike only one electron. The energleS of the election in a hydrogenlike ion are given by: -like ion is an ion containin En -(a.150 x 10"3)z* -18 %3D na where n is the principal quantum number, and Z is the atomie number. Calulate the ronization in KJ mol energy Be ion. 4 sTanif rgniticant digits. Of the 3+
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- Cesium is used extensively in photocells and in television cameras because it has the lowest ionization energy of all the stable elements. (a) What is the maximum kinetic energy of a photoelectron ejected from cesium by 520 nm light? Note that if the wavelength of the light used to irradiate the cesium surface becomes longer than 660 nm, no photoelectrons are emitted. (b) Use the rest mass of the electron to calculate the velocity of the photoelectron in (a).The energy needed to remove one electron from a gaseous potassium atom is only about two-thirds as much as that needed to remove one electron from a gaseous calcium atom, yet nearly three times as much energy as that needed to remove one electron from K+ as from Ca+ . What explanation can you give for this contrast? What do you expect to be the relation between the ionization energy of Ca+ and that of neutral K?At large interatomic separations, an alkali halide molecule MX has a lower energy as two neutral atoms, M+X ; at short separations, the ionic form (M+)(X) has a lower energy. At a certain distance, Rc , the energies of the two forms become equal, and it is near this distance that the electron will jump from the metal to the halogen atom during a collision. Because the forces between neutral atoms are weak at large distances, a reasonably good approximation can be made by ignoring any variation in potential V(R) for the neutral atoms between Rc and R= . For the ions in this distance range, Rc is dominated by their Coulomb attraction. (a) Express Rc for the first ionization energy of the metal M and the electron affinity of the halogen X. (b) Calculate Rc for LiF, KBr, and NaCl using data fromAppendix F.
- A gold nucleus is located at the origin of coordinates, andan electron is brought to a position 2 Å from the origin inthe 1y direction.(a) Calculate the force on the gold nucleus exerted by theelectron giving its components Fx and Fy.(b) Calculate the potential energy of the gold nucleus andthe electron.Q.1(a) What were the important advance (s) as a result of which, idea of an electron orbitmovement was swapped by, the notion of probability of finding electron in an orbital?What name was given to the transformed atomic model? Also explain its variouspostulates.(b) Which quantum numbers revel information about the shape, energy, orientation, andsize of the orbitals? How many orbitals are possible for n=4? Which of these may bedescribed as gerade?(c) The signs of the unsquared wave functions are usually shown in plots of the squaredfunctions. Why do you think this practice exists? Give values of angular nodes andplane of 3p, 4d, 2p, 4f, 4s.(d) Predict the trend in values of slater’s constant of the every first element of each groupof p-block elements.The contour representation zof one of the orbitals for then = 3 shell of a hydrogen atomis shown here. (a) What is thequantum number l for thisorbital? (b) How do we label thisorbital? (c) In which of the followingways would you modifythis sketch if the value of themagnetic quantum number, ml,were to change? (i) It would bedrawn larger, (ii) the number of lobes would change, (iii) thelobes of the orbital would point in a different direction, (iv)there would be no change in the sketch. [Section 6.6]
- The stratospheric ozone (O3) layer helps to protect usfrom harmful ultraviolet radiation. It does so by absorbingultraviolet light and falling apart into an O2 molecule and anoxygen atom, a process known as photodissociation.O3(g)----->O2(g) + O(g) Use the data in Appendix C to calculate the enthalpy changefor this reaction. What is the maximum wavelength a photoncan have if it is to possess sufficient energy to cause thisdissociation? In what portion of the spectrum does thiswavelength occur?At large interatomic separations, an alkali halide moleculeMX has a lower energy as two neutral atoms, M + X; atshort separations, the ionic form (M+)(X-) has a lowerenergy. At a certain distance, Rc, the energies of the twoforms become equal, and it is near this distance that theelectron will jump from the metal to the halogen atom during a collision. Because the forces between neutral atomsare weak at large distances, a reasonably good approximation can be made by ignoring any variation in potentialV(R) for the neutral atoms between Rc and R - `. For theions in this distance range, V(R) is dominated by theirCoulomb attraction.(a) Express Rc for the first ionization energy of the metalM and the electron affinity of the halogen X.(b) Calculate Rc for LiF, KBr, and NaCl using data fromAppendix F.(a) Account for formation of the following series of oxidesin terms of the electron configurations of the elementsand the discussion of ionic K2O, CaO, Sc2O3, TiO2, V2O5, CrO3. (b) Name these oxides.(c) Consider the metal oxides whose enthalpies of formation(in kJ mol -1) are listed here. Calculate the enthalpy changes in the following general reactionfor each case:MnOm(s) + H2(g)----->nM(s) + mH2O(g)(You will need to write the balanced equation for each caseand then compute ΔH°.) (d) Based on the data given, estimatea value of ΔHf° for Sc2O3(s).
- The experimental Bi¬I bond length in bismuth triiodide,BiI3, is 2.81 Å. Based on this value and data in Figure 7.7, predictthe atomic radius of Bi.To ionize Mg to Mg2+ costs two times as much energy as to form Mg+. The formation of O2- is endothermic rather than exothermic as for O-. Nevertheless, magnesium oxide is always formulated as Mg2+ O2- rather than Mg+O-a) Give theoretical reason for formulation of Mg2+O2-b) What simple experiment could be done to predict that magnesium oxide wasnot Mg+O- ?(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)?