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Encyclopedia of Physical Science and Technology EN014A-653 July 28, 2001 20:55

8 Rare Earth Elements and Materials

by simply filling the boxes beginning with that of the low- where the 54 “core” electrons are included in the sym-
est energy and continuing until the appropriate number of bol [Xe] and the number of electrons in each level is
electrons has been allotted. given by a superscript. But for element 58, Ce, the or-
The different quantum numbers together with their des- der is 6s < 4 f < 5d so the configuration for Ce is [Xe]
2
2
ignation and symbol are n, principal; l, angular momen- 6s , 4 f . This same ordering persists with minor anoma-
tum; m, magnetic; and s, spin. Quantum numbers n, l, and lies at Gd (66) and Lu (71) until the 4 f level is com-
m take only integral values and the possible values of l pletely filled with 14 electrons. The electronic configu-
and m are restricted by the value of n in a manner given rations of all of the lanthanides are shown in Table VI.
by the following relationships: Included are configurations for Sc (21) and Y (39) which
are seen to be similar to La (57). Thus it is clear why
l = 0, 1, 2,..., n − 1 there are 15 lanthanides and 17 rare earths. Sc, because it
is rather smaller in atomic and ionic size than Y and the
for given n , n
= 0
lanthanides, is sometimes excluded in the discussions that
m = +l , +(l − 1),..., −l follow.
The filling of the 4 f shell has profound consequences
for a given l there care 2l + 1 possible values of m. for the lanthanides. First there is the famous “lanthanide
1
It is found that s can have only the values ± .A contraction.” As electrons are being added to the same
2
widely used shorthand nomenclature exists to specify the level, protons are also being added to the nucleus. As elec-
angular momentum quantum number, l, according to the trons in the same level are on average the same distance
following. from the nucleus, they provide very poor mutual shielding
of the nuclear charge. Thus, as electrons and protons are
incrementally added across the series, the average radius
l Symbol
of the 4 f level decreases and, therefore, also the effective
0 s radius of the atom due to the unshielded increase in nuclear
1 p charge. This contraction is relatively small between adja-
2 d cent elements, but the cumulative effect is quite significant
3 f
4 g TABLE VI Electronic Configurations of the
. .
. . Rare Earth Elements a
. .
Element
A box or level labeled by quantum numbers n = 2,l = 1 21 Sc [Ar] 4s 3d 1
2
is thus called a 2p level, with n = 3,l = 2, we have a 3d 39 Y [Kr] 5s 4d 1
2
level, and so on. 57 La [Xe] 6s 5d 1
2
It is known that for a neutral atom in the absence of 58 Ce [Xe] 6s 4 f 2
2
electrical or magnetic fields all levels with the same n 59 Pr [Xe] 6s 4 f 3
2
and l values have the same energy (said to be degener- 60 Nd [Xe] 6s 4 f 4
2
ate levels). The number of degenerate levels associated 61 Pm [Xe] 6s 4 f 5
2
with each n ,l designation is easily computed from the 62 Sm [Xe] 6s 4 f 6
2
relationships given above. For a 2p state we find three 63 Eu [Xe] 6s 4 f 7
2
values of m, that is, +1, 0, −1 (2l + 1) which can each 66 Gd [Xe] 6s 4 f 5d 1
7
2
1
be associated with an s of ± giving a total of six 2p 2 9
2 65 Tb [Xe] 6s 4 f
levels. Similarly, a 3d level is 10-fold degenerate and a 66 Dy [Xe] 6s 4 f 10
2
4 f level is 14-fold degenerate. The precise ordering of 67 Ho [Xe] 6s 4 f 11
2
the energy states for a given atom is the result of a com- 68 Er [Xe] 6s 4 f 12
2
plex interplay of intratomic forces, but these orderings are 69 Tm [Xe] 6s 4 f 13
2
known from experiment for all elements. At element 54, 70 Yb [Xe] 6s 4 f 14
2
xenon, the energy levels are ordered in such a way that 71 Lu [Xe] 6s 4 f 14 5d 1
2
the sets 1s , 2s , 2p , 3s , 3p , 3d , 4s , 4p , 4d , 5s, and 5p are
a The symbols [Ar], [Kr], and [Xe] refer to all filled
completely filled by the 54 electrons. Beginning with el-
core energy levels associated with the elements of atomic
ement 55 (Cs) the lowest unfilled levels are the 6s , 5d,
number 18 (Ar), 36 (Kr), and 54 (Xe). Explicitly they are
and 4 f . For Cs to La, the order is 6s < 5d < 4 f and the [Ar] ≡ 1s 2s 2p 3s 3p , [Kr] ≡ [Ar] 4s 3d 4p , and
2
2
10
6
6
2
2
6
2
1
0
electronic configuration for La (57) is [Xe] 6s 5d 4 f , [Xe] ≡ [Kr]5s 5d 5p .
2
6
10