Download 1 The Energies of Electrons and Electron Configuration

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The Energies of Electrons and Electron Configuration
The energy of an electron determines its behaviour about the nucleus. Because electron energies are quantized, only certain behaviour
patterns are allowed. Descriptions of these behaviour patterns involve the use of the terms shell, subshell, and orbital. Electrons can be
grouped into shells or main energy levels, based on (energy) – (distance-from-the –nucleus) considerations. A shell contains electrons that
have approximately the same energy and spend most of their time approximately the same distance from the nucleus. The lowest energy
shell is assigned an n value of 1, the next higher shell 2, then 3, and so on. The number n is called the principal quantum number, which
represents the principal energy level. Only values of n=1-7 are used at present in designating electron shells. No known atom has
electrons that are farther from the nucleus than the 7th main energy level (n=7). The maximum number of electrons that can be found in an
electron shell varies, the higher the energy of the shell, the more electrons the shell can accommodate.
A subshell contains electrons that all have the same energy. The number of subshells within a shell depends on the n value for the shell; in
each shell there are n subshells. Subshells are identified with both a number and a lowercase letter. The four letters, s, p, d, f, denote
subshells of increasing energy within a shell. For example, 3s denotes the lowest subshell within the n=3 main shell. Subshells or
sublevels are also numbered with consecutive whole numbers starting with 0. These numbers are called the azimuthal quantum
numbers (also called the secondary quantum number in some textbooks), l . The value of l can never be greater than n -1. So,
numbered sublevels 0, 1, 2, and 3 correspond to letter designations s, p, d, and f (sharp, principal, diffuse, fundamental).
An orbital is the region of space about a nucleus where an electron with a specific energy is most likely to be found. An analogy for the
relationship between shells, subshells, and orbitals can be found in the physical layout of a high-rise condominium complex. In this analogy, a
shell is equivalent to a floor of the condominium; a subshell is equivalent to an apartment in a floor; an orbital is equivalent to a room in an
apartment. In addition to the letter designation s, p, d, or f, each orbital is given a number called the magnetic quantum number, ml . The
possible values of ml range from l to + l , including 0. The number of orbitals in a subshell varies in accordance with the values of ml ; there is
1 for an “s” subshell (0), 3 for a “p” subshell (+1, 0, -1), 5 for a “d” subshell (+2, +1, 0, -1, -2), and 7 for a “f” subshell (+3, +2, +1, 0, -1, -2, -3).
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The maximum number of electrons found in an orbital is always 2 (because its spin quantum number ( ) is restricted to + or − only).
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The notation for orbitals is the same as that for subshells.
m
The fourth quantum number is called the spin quantum number, s . Electrons not only have characteristic energies, but they also possess
another important property. They behave as though they were spinning on their own axis. The spin can be either clockwise or counter-clockwise.
A spinning charge creates a magnetic field. Thus, when a negatively charges electron spins clockwise, it behaves like a tiny magnet whose north
pole is pointing up. Counter-clockwise spin has the north pole pointing down.
In summary:
1. The principal quantum number (n) represents the average distance of the electron from the nucleus, or the size of the principal energy
level.
2.
3.
4.
The azimuthal quantum number ( l ) represents the shapes of the orbitals within an energy sublevel.
m
The magnetic quantum number ( l ) represents the orientation of the orbital in space (energy in magnetic field).
m
The spin quantum number ( s ) represents the spin of the electron (additional energy differences).
Orbitals have a definite size and shape that is related to the type of subshell in which they are found. An electron can be at only one point in an
orbital at any given time, but, because of its rapid movement throughout the orbital, it occupies the entire orbital. An analogy would be the
definite volume that is occupied by a rotating fan blade. The shapes of orbitals increase in complexity in the order s, p, d, and f. Orbitals that are
in the same subshells differ mainly in their orientation. Orbitals of the same type but in different subshells have the same general shape but
differ in size (volume). For s sublevels the shape of the electron cloud is spherical. For the s subshell in the first principal energy level, the
highest electron density is found within a sphere that is 53 picometers from the nucleus, as Bohr predicted. In the second and higher numbered
principal energy levels, the s sublevel have a high electron density at the expected distance from the nucleus of n × 53 pm . The three p orbitals
have a dumbbell shape, with the electron density being greatest in two lobes on either side of the nucleus. The 5 d orbitals in the d subshell or
sublevel have the shapes as shown. The 7 f orbitals have slightly more complex shapes than the d orbitals.
(i) 1 s – orbital:
spherical
(ii) 3 p – orbitals: dumbbell shape
(iii) 5 d – orbitals: shape as shown
(iv) f - orbital: shape as shown
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The s orbital
The simplest orbital in the atom is the 1s orbital. It has no radial or angular nodes: the 1s orbital is simply a sphere of electron density. A
node is a point where the electron probability is zero. As with all orbitals the number of radial nodes increases with the principle quantum
number (i.e. the 2s orbital has one radial node, the 3s has two etc.). Because the angular momentum quantum number is 0, there is only
one choice for the magnetic quantum number - there is only one s orbital per shell. The s orbital can hold two electrons, as long as they
have different spin quantum numbers.
The p orbitals
Starting from the 2nd shell, there is a set of p orbitals. The angular momentum quantum number of the electrons confined to p orbitals is
1, so each orbital has oneangular node. There are 3 choices for the magnetic quantum number, which indicates 3 differently oriented p
orbitals. Finally, each orbital can accommodate two electrons (with opposite spins), giving the p orbitals a total capacity of 6 electrons.
The p orbitals all have two lobes of electron density pointing along each of the axes. Each one is symmetrical along its axis. The notation
for the p orbitals indicate which axis it points down, i.e. px points along the x axis, py on the y axis and pz up and down the z axis. The p
orbitals are degenerate — they all have the same energy. P orbitals are very often involved in bonding.
2px
2py
2pz
The d orbitals
The first set of d orbitals is the 3d set. The angular momentum quantum number is 2, so each orbital has two angular nodes. There are 5
choices for the magnetic quantum number, which gives rise to 5 different d orbitals. Each orbital can hold two electrons (with opposite
spins), giving the d orbitals a total capacity of 10 electrons.
Note that all the d orbitals have four lobes of electron density, except for the dz2 orbital, which has two opposing lobes and a doughnut of
electron density around the middle. The d orbitals can be further subdivided into two smaller sets. The dx2-y2 and dz2 all point directly
along the x, y, and z axes. They form an eg set. On the other hand, the lobes of the dxy, dxz and dyz all line up in the quadrants, with no
electron density on the axes. These three orbitals form the t2g set. In most cases, the d orbitals are degenerate, but sometimes they can
split, with the eg and t2g subsets having different energy. Crystal Field Theory predicts and accounts for this. D orbitals are sometimes
involved in bonding, especially in inorganic chemistry.
The f orbitals
The first set of f orbitals is the 4f subshell. There are 7 possible magnetic quantum numbers, so there are 7 f orbitals. Their shapes are
fairly complicated, and they rarely come up when studying chemistry. There are 14 f electrons because each orbital can hold two electrons
(with opposite spins).
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Orbitals table - This table shows all orbital configurations for the real hydrogen-like wave functions up to 7s, and therefore covers the
simple electronic configuration for all elements in the periodic table up to radium. ψ graphs are shown with - and + wave function
phases shown in two different colors (arbitrarily red and blue). The pz orbital is the same as the p0 orbital, but the px and py are formed
by taking linear combinations of the p+1 and p-1 orbitals (which is why they are listed under the ml =±1 label). Also, the p+1 and p-1 are
not the same shape as the p0, since they are pure spherical harmonics.
p
(l=1)
s
(l=0)
=0
s
= -1
px
=0
pz
d
(l=2)
= +1
= -2
py
= -1
dxy
=0
dz
2
f
(l=3)
= +1
dxz
= +2
dxy
= -3
= -2
fy(3x2−y2)
fz(x2-y2)
= -1
=0
2
3
fyz
...
...
...
= +1
= +2
2
fxyz
...
...
...
fz
fxz
= +3
fx(x2−3y2)
n=
1
n=
2
n=
3
n=
4
n=
5
...
n=
6
n=
7
...
...
The Aufbau Principle
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
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More Images of Shapes of Orbitals
dxz
fy(3x2−y2)
fz(x2-y2)
dyz
fyz2
fz 3
dxy
fxz2
fxyz
fx(x2−3y2)
What are the shapes and designations of the f orbitals? The yellow and blue colors designate lobes with positive and negative amplitudes, respectively.
The 4fy3 - 3x2y orbital corresponds to n=4, =3, and
m =-3. Six lobes point to the corners of a regular
hexagon in the xy plane, with one pair of lobes
along the x-axis. Three nodal planes pass between
the lobes and intersect at the z axis.
The 4fxyz orbital corresponds to n=4, =3, and m =2. Eight lobes point to the corners of a cube, with
four lobes above and four lobes below the xy plane.
The x and y axes pass through the centers of four of
the cube's faces (between the lobes). The three
nodal planes are defined by the x, y, and z axes.
The 4f5yz2 - yr2 orbital corresponds to n=4, =3, and
m =-1. Six lobes point to the corners of a regular
hexagon in the yz plane, with one pair of lobes
along the x-axis. The three nodal planes pass
between the lobes and intersect at the y axis.
The 4f5xz2 - xr2 corresponds to n=4, =3, and
m =+1. Six lobes point to the corners of a
regular hexagon in the xz plane, with one pair
of lobes along the y-axis. The three nodal
planes pass between the lobes and intersect at
the x axis.
The 4fzx2 - zy2 orbital corresponds to n=4, =3,
and m =+2. It has the same shape as the 4fxyz
orbital, but the corners of the cube are in the
planes defined by the x, y, and z axes and the
three nodal planes cut between the lobes and
intersect along the z axis.
The 4fx3 - 3xy2 orbital corresponds to n=4, =3,
and m =+3. It is identical to the orbital with
m =-3 except that a lobe lies along the y axis
instead of along the x axis.
The 4fz3 - 3zr2 orbital corresponds to n=4, =3, and
m =0. Two lobes point along the z-axis, with two
bowl-shaped rings above and below the xy plane.
The nodal surfaces are the xy plane and a conical
surface passing through the nucleus and between
the rings and the lobes.
This diagram has some conflicts with previous diagrams on page 36 and this page and it is included here for reference only.
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The energies of electrons can be described in three ways: (i) quantum numbers; (ii) energy-level diagrams (orbital diagrams) with better
visualization; (iii) electron configuration – a more concise method. An electron configuration is a statement of how many electrons can an atom has in
each of its subshells. It indicates how many electrons of various energies an atom has. A shorthand system is used for describing electron configuration:
subshells designated using number-letter combinations are listed in order of increasing energy. A superscript following each subshell designation
indicates the number of electrons in that subshell.
(i)
Electron configuration for an atom is written in accordance with two principles and one rule:
A procedure called the Aufbau Principle is used to fill first the principal levels and their subshells (energy order). All subshells within a
given shell do not necessarily have lower energies than all subshells of higher numbered shells. Because of energy overlaps, beginning with shell 4,
one or more lower-energy subshells of a specific shell have energies that are lower than the upper subshells of a preceding shell; thus, they acquire
electrons first. The Aufbau Diagram illustrates subshell filling order for electrons. A shortcut for writing electrons configurations is to represent the
core electrons of an atom with the symbol of the preceding noble gas, for example,
( i ) Cl: 1s 2 2 s 2 2 p 6 3s 2 3 p 5 becomes Cl: Ne 3s 2 3 p 5
( ii ) Sn: 1s 2 2 s 2 2 p 6 3s 2 3 p 6 4 s 2 3d 10 4 p 6 5s 2 4 d 10 5 p 2 becomes Sn: Kr 5s 2 4 d 10 5 p 2
There is some exception to the Aufbau principle when it is applied to all known elements. Chromium and copper are the first two exceptions:
Cr (Aufbau): 1s2 2s2 2 p 6 3s2 3 p 6 4s2 3d 4 → Cr (actual): 1s2 2s2 2 p 6 3s2 3 p 6 4s1 3d 5
Cu (Aufbau): 1s2 2s2 2 p6 3s2 3 p 6 4s2 3d 9 → Cu (actual): 1s2 2s 2 2 p 6 3s2 3 p 6 4s1 3d 10
⇒
Cr: Ar 4s1 3d 5
Cu: Ar 4s1 3d 10
The evidence suggests that half-filled and filled subshells are more stable (lower energy) than unfilled subshells.
(ii) The 4th quantum number is required to satisfy Pauli Exclusion Principle, which states that no two electrons in the same atom may have the same
four quantum numbers. This means that each orbital in an atom can hold at most 2 electrons and that these electrons must have opposite spins. But
this number is not needed for the wave equations of electrons.
(iii)
Hund’s rule states that as a sublevel is filled with electrons, a single electron will occupy each orbital. Once each orbital in a sublevel contains one
electron, an additional electron will enter each orbital until every orbital has a pair of electrons that have opposite spins. This rule makes sense since
electrons repel each other strongly. This repulsion forces each electron into a separate orbital within a sublevel until each orbital has one electron. At
this point, additional electrons pair up to fill each orbital with two electrons, until the entire sublevel is filled.
Shell #
(period –
principal
#)
No. of
Subshells
Within
Shells
Maximum No. of
Electrons Within
Each Subshell
s p d
The Aufbau Principle: electrons
normally occupy the lowest energy
subshell available:
f
The Aufbau Diagram
n=1
1
2
1s2
n=2
2
2 6
2s2
2p6
n=3
3
2 6 10
3s2
3p6
3d10
n=4
4
2 6 10 14
4s2
4p6
n=5
4 (5)
2 6 10 14
5s2
n=6
3 (6)
2 6 10
6s2
n=7
1 (7)
2
7s2
No. of
subshells in
each shell =
the shell
number
No. of Orbitals
× Maximum No. of
Electrons in Each
Orbitals:
s: 1 × 2 = 2
p: 3 × 2 = 6
d : 5 × 2 = 10
f : 7 × 2 = 14
Maximum
Electron
Capacity per
shell ( 2 n 2 )
Maximum
Electron
Capacity
per element
2 × 12 = 2
2
2 × 22 = 8
10
: 8
2 × 32 = 18
28
4d10
4f14 : 18
2 × 4 2 = 32
60
5p6
5d10
5f14 : 18
2 × 5 2 = 50 *
110
6p6
6d10
2 × 6 2 = 72 *
182
2 × 7 2 = 98*
280
* the
maximum
number of
electrons in
this shell has
never been
attained in
any element
now known
2×42 =32
: 2
: 8
: 32
: 2
Total number of electrons ............ : 112
(total no. of elements now known)
Example 1. The electron configuration for
7
2
2
nitrogen ( 14.01 N ): 1s 2s 2 p
3
Example 2. The electron configuration for
11
2
2
6
1
sodium ( 22.99 Na ): 1s 2s 2 p 3s
The largest known element with 112 electrons needs only 7 principal energy levels.
Note: In order to write complete electron configurations, instead of using the Aufbau Diagram, we can also obtain the required information by
following the path of increasing atomic number through the periodic table, noting the various subshells as they are encountered.
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Table of Allowed Quantum Numbers
n
l
ml
Number of
orbitals
Orbital
Name
Number of
electrons
Total No. of Electrons
1
0
0
1
1s
2
2
2
0
0
1
2s
2
1
-1, 0, +1
3
2p
6
0
0
1
3s
2
1
-1, 0, +1
3
3p
6
2
-2, -1, 0, +1, +2
5
3d
10
0
0
1
4s
2
1
-1, 0, +1
3
4p
6
2
-2, -1, 0, +1, +2
5
4d
10
3
-3, -2, -1, 0, +1, +2, +3
7
4f
14
3
4
in Subshells
8
18
32
Orbital occupancy and the periodic table: How electron configuration rules determine the shape of the periodic table
The principal quantum number n of an orbital controls the average distance of the electron from the nucleus when it occupies that
orbital. Thus the vertical scale on the illustration below corresponds to increasing (less negative) potential energy as you go up the page.
In multi-electron atoms, repulsion between electrons causes some splitting of the orbitals having the same value of n but different
shapes (different values of l ) into different energies as shown.
The pattern of this splitting is such that d orbitals having a principle quantum number of n have energies in the same range as the s and
p orbitals belonging to the next lower value of n, or n-1. This complicates the simple picture of electron "shells" that is straightforward
for s- and p orbitals of n=1 through n=3, and it profoundly affects the organization of the periodic table.
With f orbitals, things get even more mixed up! Because of the energetic similarity of s, d and f orbitals having different values of n, the
actual electron configuration of an atom whose highest occupied orbital is in this region may change with its chemical environment. The
configurations given in tables generally refer to the isolated, gaseous atoms, and may not be representative of what occurs under more
commonly encountered conditions.
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Remember that each little box in this diagram (which
encompasses n-values 1 to 7) represents a single
orbital— a "state" of existence of an electron in an
atom, characterized by a certain energy and shape. The
shape describes how the probability of finding the
electron at any location varies with radius and angle
around the nucleus.
In the above diagram, the boxes refer to elements and not to orbitals
directly. For example, the oxygen atom, which contains four electrons
in 2p orbitals, is placed in the fourth box in the 2p group. If you think
about it, this table provides a beautiful view of how the arrangement
of the periodic table is a direct consequence of the number of orbitals
of each type and their relative energies.
Now look at the representation of the first three rows of the periodic table shown below. Electron configurations of the first eighteen
elements are shown here along with the Lewis electron-dot formulas and valence shell occupancies. Note especially the following points:
•
Orbitals fill "from the bottom up" and they occupy separate orbitals (spin unpaired) before pairing up. The latter effect is
known as Hund's rule, and it is a consequence of the smaller degree of repulsion between electrons when they can occupy
separate orbitals which have different orientations in space.
•
The up- and down-arrows represent the two possible orientations of the magnetic moment of the electron (misleadingly
known as electron "spin"), or more precisely, the two possible values of the spin quantum number. "Up" and "down" in this
context have no absolute meaning and are merely for convenience in notation. Atoms possessing unpaired electrons act as tiny
magnets and are said to be paramagnetic.
The electron dot formulas are no more than bookkeeping conveniences for counting valence shell electrons; the placement of the dots
around the symbol of the element has no significance.
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Note:
If your ion has a negative charge, add one electron to the electron configuration. If your ion is positive, subtract one electron. For
1
2
example, take Na. The electron configuration for the atom is [Ne] 3s . If you have Na- it becomes [Ne] 3s & Na+, just [Ne].
2
5
2
4
Another example, suppose you have Cl, the electron configuration is [Ne] 3s 3p . Cl- is [Ar] & Cl+ is [Ne] 3s 3p . Notice how you add
and subtract from the orbital with the highest energy.
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2
Transition Metals - You have to be careful with the transition metals. Take for example Ti, its electron configuration is [Ar] 4s 3d . Ti- is
2
3
1
2
[Ar] 4s 3d . But here is where it "can" be tricky. Ti+ is [Ar] 4s 3d . The d orbitals are written after the s, but the 4s orbitals are still of
higher energy. So you remove from them first, before the d orbitals.
In general, the octet rule works for representative metals (Groups IA, IIA) and nonmetals, but not for the transition, inner-transition or posttransition elements. These elements seek additional stability by having filled half-filled or filled orbitals d or f subshell orbitals. The octet rule
does not, however, accurately predict the electron configurations of all molecules and compounds. Not all nonmetals, nor metals, can form
compounds that satisfy the octet rule. As a result, the octet rule must be used with caution when predicting the electron configurations of
molecules and compounds. For example, some atoms violate the octet rule and are surrounded with more than four electron pairs.