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Revised August 2009
AP TOPIC 3: Electronic Configuration
Line emission spectra for hydrogen
Neils Bohr originally formulated the idea of the atom being comprised of a dense nucleus (containing protons and neutrons) being surrounded by orbiting electrons. His idea (sometimes called the solar system model) suggested that electrons could only travel in fixed orbits or shells (1, 2 and 3 etc. below) around the nucleus.
Using a device called a spectroscope it was found that gaseous elements emitted electromagnetic radiation when heated. The light emitted consisted of discrete packets of energy (quanta), and each element emitted a unique pattern of radiation. It was discovered that the release of radiation was caused by electrons in the atom absorbing energy and being promoted to a shell further away from the nucleus (say from 1 to 2 for example). When the electron falls back to its original shell (ground state) it releases the energy that it absorbed when promoted (excited state) and this creates a line in the spectrum. Since the shells are in fixed positions, the difference in energies between them, and hence the wavelength of the line in the spectra created by the electron returning to the ground state, are also fixed. This gives a unique and identifiable pattern for each element, e.g. hydrogen.
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Revised August 2009
Wave component nature of the electron
Waves and the electromagnetic spectrum Before discussing the specific nature of the wave component of electrons it is necessary to have a simple understanding of waves and the electromagnetic spectrum. All electromagnetic radiation may be considered as waves that are defined by the properties of wavelength and frequency. The wavelength () is the distance between two repeating points on a sine wave and the frequency () is the number of waves that pass a fixed point in a second. -1 Frequency is measure in s or Hertz (Hz). Equations that relate the properties of such a wave are Energy (E) h h
= Planck's constant frequency Speed of light (c) λ
= wavelength = frequency
Depending on the value of the frequency and the value of the wavelength the radiation will fall somewhere in the electromagnetic spectrum according to the diagram below.
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Revised August 2009 Wave component of electrons All the work by Bohr suggested that the electron was a discrete particle. However this did not explain several of its properties. Work by De Broglie suggested that the electron also had some wave like characteristics. The description of the electron in this way is extremely complex and requires very advanced physics, calculus and other mathematics. Schrodlinger developed this idea and solved wave equations to make predictions about where an electron may be found in an atom. The result of all this work, coupled with the Heisenberg uncertainty principle (which states that the momentum and position of an electron cannot be determined simultaneously meaning it is only possible to predict where an electron will probably be at any one time not be specific about its exact whereabouts), led to the idea of three dimensional probability maps of where any one electron may be found at any point in time within each of the fixed orbits. These three dimensional probability maps are known as orbitals.
Quantum numbers and electronic configuration
In order to bring all of this theory together the modern view of the electronic structure of the atom involves the use of four quantum numbers which taken together, help to describe that structure. Each shell has a principal quantum number associated with it. The 1st Shell has a quantum number of 1, the 2nd shell of 2 etc. In each shell, the maximum number of electrons is given by 2(n2) where n is the quantum number. Using this we find that the maximum number of electrons in each of the first four shells is; Shell and Principal Quantum number (n) 1 2 3 4
Maximum number of electrons 2 8 18 32
Each shell is further divided into sub-shells. The number of sub-shells that are possible is equal to the principal quantum number (n) and are numbered with consecutive whole numbers starting from zero. These numbers are called the azimuthal quantum numbers (l) or the angular momentum quantum numbers. In addition to the number system the azimuthal numbers are given the letters s, p, d and f corresponding to 0, 1, 2 and 3 respectively. The letters refer to the three dimensional shape of the orbital. s orbitals are spherical (soccer ball) shaped p orbitals are dumb-bell (figure of eight) shaped and align themselves on x, y and z axes d and f orbitals have more complicated shapes
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Revised August 2009 Shell and Principal quantum number (n)
Sub-shells and azimuthal quantum numbers (l)
Corresponding letter
1
0
s
2
0, 1
s, p
3
0, 1, 2
s, p, d
4
0, 1, 2, 3
s, p, d, f
Each sub-shell is further divided into orbitals. The number of orbitals that are possible is equal to twice the azimuthal quantum number plus one (2l+1). Each orbital is given a number called the magnetic quantum number (ml). Possible values of the magnetic quantum number are –l to +l including zero. Each orbital can hold a maximum of two electrons. The Pauli exclusion principle says that no one electron can have exactly the same set of quantum numbers, so since each orbital can hold a maximum of two electrons they must be distinguished between. This is done using the final, fourth quantum number the spin quantum number (ms). It can have a value of +½ or –½. Summary of quantum numbers Principal quantum number (n)
Azimuthal quantum number (l)
Sub-shell designation
Magnetic quantum number (m)
1
0
1s
0
0
2s
0
1
2p
-1, 0, +1
0
3s
0
1
3p
-1, 0, +1
2
3d
-2, -1, 0, +1, +2
0
4s
0
1
4p
-1, 0, +1
2
4d
-2, -1, 0, +1, +2
3
4f
-3, -2, -1, 0, +1, +2, +3
2
3
4
Number of orbitals in sub-shell 1 (1s) 1 (2s) 3 (2px, 2py, 2pz) 1 (3s) 3 (3px, 3py, 3pz) 5 (3dxy, 3dxz, 3dx2-y2, 3dyz, 3dz2) 1 (4s) 3 (4px, 4py, 4pz) 5 (4dxy, 4dxz, 4dx2-y2, 4dyz, 4dz2) 7 (Various names)
Number of electrons in subshell
Number of electrons in principal shell
2
2
2 8 6 2 6 18 10
2 6
10
32
14
Choice of Quantum numbers
Traditionally, when there is a choice of magnetic quantum numbers the lowest values are usually (but not always) chosen first and +½ is chosen as a spin quantum number before –½.
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Revised August 2009
Rules for filling orbitals (Aufbau process)
1. Find out how many electrons are present (Refer to the atomic number of the atom and then consider any charge present caused by the loss or gain of electrons). 2. Lowest energy orbitals are filled first. The orbitals have ascending energies with 1s having the smallest energy, 2s the next etc. There is a minor complication here, the 4s orbital has a slightly lower energy than the 3d orbitals and as a result the 4s orbital is filled before the 3d orbitals. Similarly the 5s orbital has a slightly lower energy than the 4d orbitals and as a result the 5s orbital is filled before the 4d orbital. 3. Hund’s rule of maximum multiplicity states that if there is more than one orbital with the same energy (degenerate) then one electron is placed into each orbital before any pairing takes place. All similar orbitals have a similar energy, e.g. all three 2p orbitals have the same energy and are said to be degenerate E.g. if there are three electrons to be placed into the 2p orbitals one would enter the x, one would enter they y and one would enter the z before any were paired in the x, y or z.
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Revised August 2009 Using the periodic table to determine electronic configuration This is an extremely powerful tool and requires a slight, but significant modification of the periodic table. In the table below, Hydrogen and Helium have been moved into groups 1 and 2 respectively. This is only for the purpose of determining electronic configuration and is NOT appropriate in other circumstances (although H will sometimes appear at the top of group 1).
Period
1 2
3
4
5
6
7
Group 1 2 s BLOCK 1 2 H He 1 4 3 4 Li Be 7 9 11 12 Na Mg 23 24 19 20 K Ca 39 40 37 38 Rb Sr 86 88 55 56 Cs Ba 133 137 87 88 Fr Ra 223 226
T HE
PER IODIC
T ABLE 13
14
Group 15 16 p BLOCK
5 B 11 13 Al 27 31 Ga 70 49 In 115 81 Tl 204
6 C 12 14 Si 28 32 Ge 73 50 Sn 119 82 Pb 207
7 N 14 15 P 31 33 As 75 51 Sb 122 83 Bi 209
d BLOCK
T
21 Sc 45 39 Y 89 57 La* 139 89 Ac** 226
R
A
22 Ti 48 40 Zr 91 72 Hf 178
N
S
23 V 51 41 Nb 93 73 Ta 181
I
T
I
24 Cr 52 42 Mo 96 74 W 184
O
25 Mn 55 43 Tc 99 75 Re 186
N
26 Fe 56 44 Ru 101 76 Os 190
M
E
27 Co 59 45 Rh 103 77 Ir 192
T
A
28 Ni 59 46 Pd 106 78 Pt 195
L
29 Cu 64 47 Ag 108 79 Au 197
S
30 Zn 65 48 Cd 112 80 Hg 201
8 O 16 16 S 32 34 Se 79 52 Te 128 84 Po 210
To determine the electronic configuration of any element, build the electronic configuration by following the steps below. 1. The period number shows the shell (principal quantum) number. NOTE: When filling the d orbitals subtract one from the principal quantum number to determine the correct shell. 2. The block shows the type of orbital. 3. Then add one electron for each element until the orbital, then sub-shell and ultimately the shell, is full. 4. Record the electronic configuration in the format; shell (principal quantum) number, block (orbital), number of electrons (as a superscript). E.g. Hydrogen has one electron that is found in the s orbital in the first shell hence
1s1
(pronounced “one s one”)
Helium has two electrons that are found in the s orbital in the first shell hence
1s2
(pronounced “one s two”)
Examples Element F P Sb
# of electrons 9 15 51
Electronic Configuration 2
2
5
1s 2s 2p 1s2 2s2 2p6 3s2 3p3 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p3
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Notes 2
2
1
1
1
1
1
1
1
Actually (2px 2py 2pz ) Actually (3px 3py 3pz ) Actually (5px 5py 5pz ) Page 6 of 12
17
18
9 F 19 17 Cl 35.5 35 Br 80 53 I 127 85 At 210
10 Ne 20 18 Ar 36 36 Kr 84 54 Xe 131 86 Rn 222
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Revised August 2009 Task 3a 1. Fill in the table below. ATOMIC NUMBER
SYMBOL
NUMBER OF ELECTRONS
1
H
1
2
He
2
3
Li
3
4
Be
4
5
B
5
6
C
6
7
N
7
8
O
8
9
F
9
10
Ne
10
11
Na
11
12
Mg
12
13
Al
13
14
Si
14
15
P
15
16
S
16
17
Cl
17
18
Ar
18
ELECTRONIC CONFIGURATION 1s1
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Revised August 2009 ATOMIC NUMBER
SYMBOL
NUMBER OF ELECTRONS
19
K
19
20
Ca
20
21
Sc
21
22
Ti
22
23
V
23
24
Cr
*
24
25
Mn
25
26
Fe
26
27
Co
27
28
Ni
28
29
Cu
*
ELECTRONIC CONFIGURATION
29
30
Zn
30
31
Ga
31
32
Ge
32
33
As
33
34
Se
34
35
Br
35
36
Kr
36
The anomalies of Cr and Cu are easy to explain once you know that a half-filled or completely filled d shell is considered to have extra stability. Hence configurations ending 4s1 3d5 and 4s1 3d10 rather than 4s2 3d4 and 4s2 3d9 are considered to be preferable. In each case one of the s electrons is promoted to the d shell to create a more stable configuration. C:\www.adriandingleschemistrypages.com\apnotes\apnotes03.doc
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Revised August 2009 Noble gas core method It can be seen from the table above that this method of writing electronic configurations can be extremely long winded. In order to simplify the process the noble gas core method can be employed. In this method the electronic configuration is determined by writing the previous noble gas in square brackets and then filling orbitals as before. E.g. Phosphorus becomes, [Ne] 3s2 3p3 Since Ne is the previous noble gas to phosphorus and the following electrons are in the 3s and 2 2 6 3p sub-shells respectively. In this case this eliminates the need to write 1s 2s 2p for Ne therefore shortening the notation. Task 3b 1. Write the electronic configuration of the following elements using the noble gas core method. (i) (ii) (iii) (iv) (v) (vi)
Cu Co Ca C Ar Ga
2. Write the electronic configuration of the following simple ions using the noble gas core method. (i) (ii) (iii) (iv) (v)
FCa2+ S2Na+ Al3+
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Revised August 2009 Electrons in boxes notation So far we have seen how to write electron configurations in the traditional long hand method and with the shortened noble gas core method. You should be familiar with one final method of displaying electronic configurations. Consider the examples below.
C
N
O
F
Ne
In these examples arrows represent the electrons and boxes represent the orbitals. As you can see the three, 2p orbitals avoid having electrons paired until it is absolutely necessary. In the notation discussed previously nitrogen could be represented in one of four ways. 1st way 2nd way
1s2 2s2 2p3 1s2 2s2 2px1 2py1 2pz1
3rd way 4th way
[He] 2s2 2p3 [He] 2s2 2px1 2py1 2pz1
In the 2nd and 4th ways the three, 2p orbitals are broken down to show the separation of electrons within the orbitals. The five d orbitals can be represented in a similar way; so, an atom with electronic structure ending in d5 would be represented thus,
and one ending in d8, thus,
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Revised August 2009 Task 3c Using the blanks below complete the electronic configurations for the elements listed.
1s
2s
2p
3s
3p
3d
4s
4p
Element
C 1s
2s
2p
3s
3p
3d
4s
4p
Element
Ca 1s
2s
2p
3s
3p
3d
4s
4p
Element
Ne 1s
2s
2p
3s
3p
3d
4s
4p
Element
Cr 1s
2s
2p
3s
3p
3d
4s
4p
Element
Ga 1s
2s
2p
3s
3p
3d
4s
4p
Element
K 1s
2s
2p
3s
3p
3d
4s
4p
Element
Ni 1s
2s
2p
3s
3p
3d
4s
4p
Element
N 1s
2s
2p
3s
3p
3d
4s
4p
Element
Sc 1s
2s
2p
3s
3p
3d
4s
4p
Element
Kr
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Revised August 2009
Other aspects of electronic configuration
Paramagnetism & Diamagnetism Paramagnetic species are those that are attracted by a magnet and are created when unpaired electrons are present in an atom. Diamagnetic species are slightly repelled by magnets and occur when all electrons are paired. Rydberg equation The Rydberg equation is used to calculate the energy changes when electrons are promoted to higher energy levels and subsequently fall back to the lower energy levels. E
2.178 x 10 -18 n2
E = the energy associated with a particular quantum number, n. By calculating the energies associated with two different quantum levels and finding the difference, one can calculate the energy required to promote an electron from one level to another, or calculate the energy released when an electron falls back from a higher level to a lower level. Energy changes during transitions are proportional to (atomic #)2. This means that if an electron is promoted from for example level 1 to level 5 in a species that has less protons in the nucleus the same transition for a species with more protons would be more difficult. This is because the protons in the nucleus are attracting the electron to the lower energy level and more energy is required to promote them. Consequently a greater amount of energy is released from the species with the larger number of protons when the electron falls back to the original level. d block metal ions When forming positive ions, d block elements lose their outer s electrons before any d electrons. Isoelectronic species Isoelectronic species have the same electronic configuration. As a result they must be distinguished by some other means, for example the number of protons present.
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