Biomedical Engineering Reference
In-Depth Information
back of this topic, to which the reader is referred in this discussion. The first period
contains only hydrogen and helium.
The next element, Li, has three electrons. Two occupy the full K shell and the
third occupies a state in the L shell
(
n
= 2)
. Electrons in this shell can have
l
= 0
(s states) or
l
= 1
(p states). The 2s state has lower energy than the 2p, and so the
electron configuration of Li is 1s
2
2
s
1
.With
Z
= 4
(Be), the other 2s state is occupied,
and the configuration is 1s
2
2
s
2
. No additional s electrons
(
l
=
0)
can be added in
these two shells. However, the L shell can now accommodate electrons with
l
=
1
(p electrons) and with three values of
m
:
-1, 0, +1
. Since two electrons with opposite
spins (spin quantum numbers
±
1
2
) can occupy each state of given
n
,
l
,and
m
, there
can be a total of six electrons in the 2p states. The configurations for the next six
elements involve the successive filling of these states, from
Z
=
5
(B), 1s
2
2
s
2
p
1
,
to
Z
10 (Ne), 1s
2
2s
2
p
6
. The noble gas neon has the completed L shell. To save
repeating the writing of the identical inner-shell configurations for other elements,
one denotes the neon configuration by [Ne]. The second period of the table begins
with Li and ends with Ne.
With the next element, sodium, the filling of the M shell begins. Sodium has
a 3s electron and its configuration is [Ne]3s
1
. Its single outer-shell electron gives
it properties akin to those of lithium. One sees that the other alkali metals in the
group IA of the periodic table are all characterized by having a single s electron in
their outer shell. The third period ends with the filling of the 3s
2
p
6
=
levels in the
noblegas,Ar
(
Z
18)
. The chemical and physical properties of the eight elements
in the third period are similar to those of the eight elements in the second period
with the same outer-shell electron configurations.
The configuration of Ar
(
Z
= 18)
, which is [Ne]3s
2
p
6
, is also designated as [Ar].
All of the states with
n
= 1
,
l
= 0
;
n
= 2
,
l
= 0, 1
;and
n
= 3
,
l
= 0, 1
are occupied in
Ar. However, the M shell is not yet filled, because d states
(
l
= 2)
are possible when
n
= 3
. Because there are five values of
m
when
l
= 2
, there are five d states, which
can accommodate a total of ten electrons (five pairs with opposite spin), which is the
number needed to complete the M shell. It turns out that the 4s energy levels are
lower than the 3d. Therefore, the next two elements, K and Ca, that follow Ar have
the configurations [Ar]4s
1
and [Ar]4s
2
. The next ten elements, from Sc
(
Z
=
=
21)
through Zn
(
Z
=
30)
, are known as the transition metals. This series fills the 3d
levels, sometimes in combination with 4s
1
and sometimes with 4s
2
electrons. The
configuration of Zn is [Ar]3d
10
4s
2
, at which point the M shell (
n
3) is complete.
The next six elements after Zn fill the six 4p states, ending with the noble gas, Kr,
having the configuration [Ar]3d
10
4s
2
p
6
.
After Ar, the shells with a given principal quantum number do not get filled
in order. Nevertheless, one can speak of the filling of certain subshells in order,
such as the 4s subshell and then the 3d in the transition metals. The lanthanide
series of rare-earth elements, from
Z
=
=
58
(Ce) to
Z
=
71
(Lu), occurs when the 4f
subshell is being filled. For these states
l
=
14
elements compose the series. Since it is an inner subshell that is being filled,
these elements all have very nearly the same chemical properties. The situation is
=
3
, and since
-3
≤
m
≤
3
, a total of
7
×
2
