BioPHYSICAL chemistry

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four quantum numbers, with each orbital having one spin up and one
spin down electron. Thus, for hydrogen, the single electron will be located
in a 1s orbital. The two electrons present in helium will also be in the
1s orbital. The arrangement of the electrons in the orbitals, the elec-
tron configuration, is denoted for hydrogen and helium as 1s^1 and 1s^2 ,
where the superscript identifies the number of electrons in the orbital.
In general, only the outermost orbitals are shown as the inner orbitals are
assumed to be filled. For example, lithium has three electrons. Two will
be present in the 1s orbital and complete that shell and the third must be
present in an n=2 orbital. The electron configuration is denoted by 2s^1 ,
showing only the 2s state and not the inner 1s state. In the hydrogen
model all of the n=2 orbitals, the 2s and the three 2p orbitals, all have
the same energy. However, the energies of these orbitals are modified due
to the presence of more than one electron. As discussed above, one of the
major effects is the shielding of the outer electrons, with the inner elec-
trons modifying the effective nuclear charge. The extent of this shielding
on the 2s and 2p orbitals differs. An electron in the 2s orbital has a greater
presence near the nucleus; that is, a greater probability of being near
the nucleus, than an electron in a 2p orbital. As a result of the greater
presence, the electron in the 2s orbital experiences less shielding due to
the 1s electrons. Consequently, the electron in the 2s orbital experiences
a greater nuclear charge and is held more tightly than one in a 2p orbital.
This corresponds to an electron in a 2s orbital having a lower energy than
one in a 2p orbital. Consequently, the third electron will occupy the 2s
orbital rather than one of the 2p orbitals.
The three p orbitals can hold up to six electrons. When more than
one electron is present in a p orbital the electrons are expected to fill
different p orbitals to minimize the repulsive electrostatic interaction by
maximizing the distance between the electrons. For example, carbon has
a total of six electrons, with two in the 1s orbitals, two in the 2s orbitals,
and two in the 2p orbitals. The two electrons in the 2p orbitals are expected
to occupy two different 2p orbitals of the three available. For nitrogen,
the three electrons in the 2p orbitals will be in the each of the three orbitals.
According to Hund’s rule, the electrons in the 2p orbitals will prefer-
entially prefer a configuration in which the spins are all aligned with the
greatest number of unpaired electrons. The 2p electrons are filled in neon
that has a total of 10 electrons with six in the 2p orbitals.
In potassium, the unpaired electron is located in a 4s orbital rather
than a 3d orbital. Likewise, calcium has two electrons in the 4s orbital.
The lower energy of the 4s orbital compared to the 3d orbital arises
from the greater probability of an electron in the 4s orbital being near
the nucleus and hence increasing its interactions with the nucleus. Finally
with scandium, electrons begin to occupy the 3d orbitals. This begins the
transition metals that are among the heaviest atoms found in proteins,
including manganese, iron, nickel, copper, and zinc.

266 PART 2 QUANTUM MECHANICS AND SPECTROSCOPY

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