1. Which of the following corrrespond to spherical total electron
distributions?
a. 1s2,2s1 b. 1s2,2s2,2px12py12pz1
c. 1s2,2s2,2p2 d. [Ar]4s2,3d1
e. [Ar]4s2,3d5 f. Fe2+
g. Eu2+ h. Cu2+
Any subshell (set of orbitals with the same principal quantum number and letter) which is filled or half filled has a spherical total electron distribution. E.g. 4p2 is not but 2p3 and 3p6 are spherical. So the totally spherical electron distributions are:
a, b, e, & g. (g is [Xe]6s2,5f7)
2. "Bond order" is a term used to indicate the net bonding pairs present between two atoms. Electrons in bonding orbitals count 1/2 each, and electrons in anti-bonding orbitals count -1/2. (There are also non-bonding electrons in some systems, which do not count at all. Core electrons, i.e. those not in the valence shell, are generally considered non-bonding)
What are the orders of the bonds in the following molecules? a. H2+ b. He2+ c. Na2 d.Be2
2s atomic orbitals combine to make s(2s) and s*(2s) molecular orbitals just like the 1s do, so the energy level diagrams (not to scale!)for the four species are:
H2 He2+ Na2 Be2
anti- sig*(1s) | sig*(1s) sig*(2s) || sig*(2s)
bonding
bonding | sig(1s) || sig(1s) || sig(2s) || sig(2s)
bond 0.5 0.5 1 0
order
Experimentally H2+ and He2+ are known and have similar bond lengths
and dissociation energies. Na vapour at the boiling point is found to
contain a small (5-10%) amount of Na2 molecules but there is no evidence
for the existence of Be2. All this can be explained by the above
molecular orbital energy diagrams.
3. The 3s and 3d orbitals of hydrogen are degenerate, but for a
polyelectron atom like Ca the 3d orbitals have about the same energy as
the 4s.
a. The evidence comes from two sources:
1. The actual energy levels can be worked out from the atomic spectra of the elements.
2. The chemical evidence that the transition series (due to the filling of the 3d orbitals) begins after calcium (4s filled) and not after argon. I.e. the evidence is the periodic table itself.
b. The explanation is to do with the radial distributions of electrons in the various types of orbital (See diagram in text or class notes). A 3s electron penetrates the electronic core of the atom (inner electron cloud) more than a 3d electron would so it, on average experiences a larger effective nuclear charge. Or, in other words, the 3s is less screened from the nucleus by the inner electrons than the 3d. The more screened 3d electron "sees" a smaller effective nuclear charge and is higher in energy (the electrostatic energy is proportional to the product of the charges.) A 3p electron is somewhere in between these two, so the order of energies is 3s<3p<3d.
c. The d block elements occuring where they do in the periodic table. I.e. after Ca, rather than after Ar.
d. See my answer to part b.
(C) H.J Clase 1999 - Updated 1999.02.03