Question

please show all work for E9D.5 (b)

- TOT AT DITT TOT TTTOO CITTTTTT ADOTTAT TOT OT TITTTTTTTTTT E9D.5(a) Estimate the orbital energies to use in a calculation of the molecular orbitals of HCl. For data, see Tables 8B.4 and 8B.5. Take B= -1.00 eV. E9D.5(b) Estimate the orbital energies to use in a calculation of the molecular orbitals of HBr. For data, see Tables 8B.4 and 8B.5. Take B = -1.00 eV.

Answer 1

Background Information:

The ionization energy is opposite in sign to the orbital energy of the electron (Koopman's theorem)

For single-electron atoms such as hydrogen, the atomic orbital energy is dependent on principal quantum number only. It is given by the formula:

E_n = -k.Z²/n²;

where k is a constant whose value is 2.179 × 10-18 J or 13.6 eV

Z is the atomic number and n is the value of the principal quantum number.

For muti-electron atoms, the approximate energy can be calculated by using the following formula:

E_n = -.Z²_eff/n²; where Z_eff is the effective nuclear charge on that electron

E9D.5 (a):

For hydrogen atomic orbital energy of its single 1s electron is its ionization energy but with opposite sign. This is because of the fact that when an electron is knocked out from an atom, its energy becomes zero. Therefore, the sum of the energy required to knock-out an electron and its orbital energy must be zero.

Hence orbital energy of 1s electron in H = -1312.0 kJ/mol

For orbital energies of Cl atom, let's consider its electronic configuration

₁₇Cl: 1s² 2s² 2p⁶ 3s² 3p⁵

The effective nuclear charge can be calculated for electrons in each of the orbitals using Slater's rule and then the formula given in the background to this question can be used to calculate orbital energies. There are 5 different types of electrons in Chlorine atom.

For example, if we want to calculate effective nuclear charge for 3p electrons, we can do as follows:

contribution of each of the 3rd shell electrons = 0.35

contribution of each of the 2nd shell electrons = 0.85

contribution of each of the 1st shell electrons = 1

Therefore Z_eff for each of the 3p electrons = Z - S; where Z is the atomic number and S is the shielding provided by electrons in same or lower shells than the electron for which we want to calculate Z_eff

In this case Z_eff = 17 - [6(0.35)+8(0.85)+2(1)] = 17-10.9 =6.1

Now the energy associated with 3p orbital electrons can be calculated. Z_eff can be found for 3s, 2p, 2s, and 1s electrons separately leading to finding orbital energies

E9d.5(b):

The atomic orbital energy for H atom remains same.

The atomic orbital energies for electrons in different orbitals of bromine atom can be calculated after calculating Z_eff for each set of orbitals.

The electronic configuration of Bromine is given below:

Br: (1s²)(2s²sp⁶)(3s²3p⁶)(3d¹⁰)(4s² 4p⁵)

Note: for d electrons, the lower electron's contribution is 1