1. Simon:
(a) Let us approximate an electron in the n-th shell of an atom as being like an electron in the n-th shell of a hydrogen atom with an effective nuclear charge Z. Use your knowledge of the hydrogen atom to calculate the ionization energy of this electron (i.e., the energy required to pull the electron away from the atom) as a function of Z and n.
(b) Consider the two approximations discussed in class for estimating the effective nuclear charge:
Z= Zn- N‹
Z = Zn- N< -(No-1)/ 2,
where Zn is the actual nuclear charge (or the atomic number), N< is the number of electrons in shells inside of n (i.e., electrons with principal quantum numbers less than n) and No is the total number of electrons in the n-th principal shell (including the electron we are trying to remove from the atom).
(i) Explain the reasoning behind these two approximations.
(ii) Use these approximations to calculate the ionization energies for the atoms with atomic number 1 through 21. Make a plot of your results and compare them to the actual ionization energies (you will have to look these up on a table) .
(iii) Comment on how accurate your approximations are compared to the tabulated results.
(iv) The above approximations begin to break down for higher atomic numbers. Why is this?
3. Simon: The diagram below shows a plan view of a structure of cubic ZnS (zincblende) looking down the z axis. The numbers attached to some atoms represent the heights of the atoms above the z = 0 plane expressed as a fractional of the cube edge length
a. Unlabeled atoms are at z = 0 and z = a.
(a) What is the Bravais lattice type?
(b) Describe the basis.
(c) Given that a = 0.541 nm, calculate the nearest-neighbor Zn-Zn, Zn-S and S-S distances.
