[marky6]

I would like to ask for your help with the following questions, please:

Part A: True or False

1. The total wave function is the product of the angular and radial parts. I think this is definitely true.

2. The solutions to the angular part of the wave function are dependent on n. I do not know, honestly, l and m do depend on n and are the results from the angular part, but does that mean the angular wave function depends on n, too?

3. For hydrogen, orbitals with the same value are degenerate. Well, if n is 1, they are since n=1 gives rise to s orbitals only, but what about n=2, are there 2s and 2p orbitals in hydrogen?

4. P-orbitals are centrosymmetric. I have no idea what centrosymmetric means. I have not found it in my textbook nor anywhere in the www.


Part B -  an open question:

What four conditions are the solutions to the Schroedinger equation bound by and why?

I found in the lecture notes the following, but have no idea whether one may call these statements "boundaries":

1. The solutions must be normalised (the sum of the probabilities over all points must equal 1) because the electron must be somewhere.
2. The function must be continuous, for all waves are continuous.
3. The function must be single valued so that each set of points gives one probability only.
4. The function must be finite since the electron must definitenly be somewhere.


Part C - line formulae, nomenclature and isomerism of transition metal complexes:

I wonder in which order the following ligands need to be listed in the line formula:

Ammine (NH3), ethyleneamine (en), pyridine (py) and bipyridine (bipy) since the ligating atom in each of these cases is N.

For instance, is diammine dibromo bispyridine manganese iii bromide
[Mn (Br)2 (py)2 (NH3)2] Br
or
[Mn (Br)2 (NH3)2 (py)2] Br?

And is diammine bisethylenediamine chromium iii hexacyano ferrate ii
[Cr (en)2 (NH3)2]4 [Fe (CN)6]3
or
[Cr (NH3)2 (en)2]4 [Fe (CN)6]3?

Moreover, I wonder how to place cis and trans in a name.

Is the correct name for
cis, fac [Co (Br)2 (N(CH3)2) (NH3)3]
fac, cis-triammine dibromo dimethylamido cobalt iii 
or is it
fac trisammine cis dibromo dimethylamido cobalt iii?

Is the correct name for
trans, cis, cis [Fe (Br)2 (NH3)2 (OH2)2] NO2
trans, cis, cis-diammine diaqua dibromo iron iii nitrite 
or is it
cis diammine cis diaqua trans dibromo iron iii nitrite?

I would be so grateful for your help, please. 

[tomothyengel]

Part A
1. I'd agree.
2. For a hydrogen-like atom, the angular part of the wavefunction is only directly dependent upon l and m for the stationary states. Although obviously for the overall state, the value of l and thus m are restricted by the value of n.
3. For a hydrogen (or any one electron, one nucleus system) without making relativistic, spin-orbit coupling and other corrections to the orbitals (so in their simplest form) the energy of the orbitals only depend on the n principal quantum number. The energy formula is the same as that predicted by the Bohr atom model. However, things get more fiddly if you break the symmetry of the potential (i.e. by adding another electron in the system) or when you start accounting for relativistic effects and spin-orbit coupling. The latter two effects, for hydrogen-like atoms are typically quite small in comparison with the divisions between the energies of different principal quantum numbers (it's in the order of something like 1000 times smaller). However, for hydrogen-like atoms with greater nuclear charge (e.g. He+ or Li 2+), relativistic and S-O coupling effects become more pronounced.
4. My guess is as good as yours.

Part B
1. The wave function must be continuous, and their gradients must also be continuous. One possible justification is that the kinetic energy is related to the curvature of the wave function, if the wave function were not continuous, it would have have infinite curvature, which would result in infinite speed etc. popping up which is problematic at best.
2. The wave function must be single valued, becuase it corresponds to a probability amplitude, thus as you said, there can only be a single probability of finding something somewhere.
3. The wave function must be normalisable; that means that its square modulus must have a finite integral over all space. This is related to the probability interpretation of the wavefunction- there must be a finite probability of finding the particle somewhere.
4. You could split 1. into continuous wave function and continuous derivative (gradient).

I'm afraid I can't help you with part C, not really my area of expertise, but I hope this helps. (:

[Enthalpy]

1. I'd agree as soon as the potential results from one central charge. Not in a molecule.
3. Hydrogen has the complete set of orbitals. If some day you find a single hydrogen atom (try in interstellar medium), its electron will likely be on 1s.
4. Do I understand "centrosymmetric" as a spherical symmetry? Then, no. p orbitals have a cylindrical symmetry, despite the potential has a spherical symmetry. That is, they introduce one axis along which the orbital momentum is known, which reduces the symmetry.

I'd like to recommend the nice orbital pictures there:
http://winter.group.shef.ac.uk/orbitron/
http://winter.group.shef.ac.uk/orbitron/AOs/2p/index.html
(notice the 2p here have zero angular momentum along the known direction, but other solutions hence shapes exist, as a doughnut then, with the phase moving 360° per turn instead of + and -)

[marky6]

Great thanks to both of you. You help has been cool.