Re: Periodic table

I am a little handicapped in answering this by your failure to provide a
'grade level'. Even if you are not attending school, it is useful to know
at what level to pitch an answer. I am assuming that your knowledge of
Chemistry is fairly sophisticated.

The term 'valence shell' electrons refers specifically to any electrons
in an atom that are sufficiently loosely bound to the atom to become
involved in chemical reactions and chemical bonding. 'Outer electrons'
can mean different things in different contexts. But in terms of the
simple meaning of language, it ought to mean those furthest (on average)
from the atomic nucleus. Sometimes 'outer electrons' and
'valence shell electrons' are presumed to mean exactly the same thing. But
if you were going to make a distinction, then taking an example like nickel
Ni = [Ar] 3d8 4s2 , it would be possible to refer to nickel as having 10 
valence shell electrons, but only 2 outer electrons. On average, the 4s
electrons are much the same distance from the nucleus as the 3d electrons,
but the 4s electrons make more frequent excursions to great distances from
the nucleus. (They match on average because they also spend more of their
time close to the nucleus than 3d electrons.)

The bismuth example that you give is a very complicated one indeed. The 
electron configuration is [Xe] 4f14 5d10 6s2 6p3. In a neutral bismuth atom,
a 4f or 5d electron is easier to remove than a 6s electron, though not as
easy to remove as a 6p electron. Yet 4s and 5d
electrons do not usually become involved in the chemistry of bismuth. In 
most of its chemistry bismuth shows a valency of 3, and it would be
reasonable to consider only the 6p electrons as valence electrons. But if
bismuth becomes ionised (loses electrons) or strongly polarised by bonding
to electronegative elements like O, F, or Cl, then the 4f and 5d electrons 
become much more strongly bound, while the 6s electrons remain loosely 
bound, and can get involved in the chemistry. Even so, the oxidation state
of +5 for bismuth is fairly unusual, and it is really only in BiF5 that
there is a clear-cut valency of 5. (Valency and oxidation number are again
two similar, but slightly different things - that is another story).

Your second query relates to the filling order of electron shells. I think 
that the specific sort of problem you have in mind is that, for example,
vanadium has the ground state configuration [Ar] 3d3 4s2, while chromium has
[Ar] 3d5 4s1. The short answer is that there are no rules. If you tried to
formulate them, there would be nearly as many rules as problematic elements,
and that goes against the nature of a rule as a useful generalisation. 

I can give you some insight as to why the irregularities arise, and what the
problem is. The ground state of the carbon atom has the configuration
[He] 2s2 2p2. But the two p electrons interact with one another, and they 
can be put into the atom in several different ways. Obviously if they both
went into, say, the px orbital, then the energy would be higher than if one
went into px and one into pz (because they repel one another, and they would
have many more close encounters if they both went into the same orbital!)
When the situation is worked out properly, we find that there are three
different energy levels corresponding to the 2s2 2p2 configuration, known as
triplet-P, singlet-D, and singlet-S.

A similar situation arises every time you have a partly filled valence shell.
If you have a situation like d3 or d5s1 , there are a large number of energy
levels associated with the configuration, and a very complicated pattern of 
energy splittings.

With chromium, whose ground state is d5s1 when you might have expected it to
be d4s2, there are many energy levels associated with each of these
configurations. The d4s2 configuration is actually slightly lower in energy
than d5s1. But when all of the splittings are taken into account we find that
the detail of the splitting patterns is such that one of the d5s1 levels
falls lower than any of the d4s2 levels, even though the average of all of
the d5s1 levels is higher than the average of all of the d4s2 levels. This
very low energy d5s1 level arises from putting one electron in each of the
five d orbitals, all with spins parallel, and the single s electron also 
spin parallel. It is known as septet-S.

All three transition series are slightly different. In the second transition
series (Y to Cd) an electron has more tendency to go into a d orbital
rather than the s orbital, while the third transition series, is broadly 
similar to the first, but Ni and Pt differ in one direction while Cr and W
differ in the other! The lanthanides and actinides are also quite different
from one another.

The actual configurations themselves are obtained from a very careful and
detailed analysis of the atomic spectrum of the element. Sometimes the
photoelectron spectrum can also be used to help with the analysis.

John.