Module 1 : Atomic Structure
Lecture 6 : Multi-Electron Atoms
  6.9

Exercises

6.1) The ionization energy (IE) of an atom is defined as the minimum energy required to ionize the atom A A+ + e, I.E = E(A+) - E(A) . Look up the ionizaton energies of atoms hydrogen to argon and explain the trend in their values using the ideas developed in this lecture.

 
6.2) What is the electronic configuration of atoms with atomic numbers 19, 24, 29, 42, 64 and 103 ?

 
6.3) Write the electronic Schrödinger equation for Li and Be atoms.


6.4) Electrons and other microscopic objects are not distinguishable from each other, ie , it is not correct to label the first electron as 1 and the second one as 2. For spin 1/2 particles such as an electron, the total wavefunction is antisymmetric, ie, it changes sign when the electron labels 1 and 2 are interchanged. A correct wavefunction for He is
(1, 2) = 1 (r1) 2 (r2) - 1 (r2) 2 (r1). Veriy that

(1, 2) = - (2, 1). Construct antisymmetric functions for (1, 2, 3)
 

6.5) The nuclear charge on H is 1. For He, each electron does not experience the full nuclear charge of 2 because this nuclear charge is screened by the second electron. Using the Bohr like formula,

I.E = Z2eff (I.E)H / n2, calculate the effective nuclear charge for He and Li+. Here, (I.E)H = ionization energy of H = 13.6 eV, or 1.313 x 106 J/mol, n = the principal quantum number of the electron and Zeff = effective nuclear charge. The ionisation energies of He and Li+ are 2.372 and 7.3 MJ/mol respectively (1 MJ = 106 J).
The screening of the nuclear charge by other electrons is given by the screening constant, S which is defined by Zeff = Z - S. Calulate Zeff for He and Li+ .
 
6.6) Distinguish between probability density and electron density.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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