A second
electron added to a hydrogen atom will see both the
charge of the proton as well as the charge of the first
electron. Altough a second electron can be slightly
bound, one can obviously not add electrons indefinitely
(In fact two is the most). Heavier nuclei, which have a
larger number For our
purposes, we will talk about energy levels of electrons
in atoms without considering the effects of other
electrons. The other electrons will for the most part
rearrange the energy levels somewhat, but for purposes of
classification and insight, it is good to classify the
orbitals as if the other electrons were not there. The
labels are the For one
electron in the vicinity of a single nucleus of charge , n,
lm_{l}
and m_{s}.
The first number gives
information about the energy of the orbital. Roughly, it
describes the number of nodes in the wave function. The
lowest energy level has n = 1,
and the binding energy of the orbital falls inversely
proportional to nn^{2}. The second
numbers m_{l}
give information about the angular momentum of the state.
Both are always integers. The angular momentum m_{l
}is in integral units of h/2 but never exceeds + p
and never goes below -l. For
instance if l equals 3, lm_{l
}can take on the seven values,
-3,2,-1,0,1,2,3. The values of
can be from zero to l.
There are therefore (2n - 1 + 1)
values of lm_{l }for
each . The last quantum number
lm_{s }is
always +1/2 or -1/2, thus there are always two such
numbers.Due to the
screening of other electrons the energies of various
levels picks up a dependence on . The levels are
then denoted by n and n,
and the two numbers lm_{l
}and m_{s
}will be neglected except in knowing
the number of different states that have a fixed and n
. That
degeneracy is lThe factor of
two comes from the two values of will have
somewhat lower energy. For instance, if one considers an
iron atom with 26 electrons, the electron shells for nthat are: n
< 5
If an atom had a
given number of electrons |