Quiz 2/ A/ How many orbitals are possible for n=3? B/ How many orbital nodes do 2S ,3P ,4d and 5f orbitals exhibit?
11/11/2016 Dr. Mohammed H. Said 1 lecture 2 Effective nuclear charge
The effective nuclear charge is the net positive charge experienced by an electron in a multi-electron atom
Effective Nuclear Charge Diagram
11/11/2016 Dr. Mohammed H. Said 2 Calculating the effective nuclear charge In an atom with one electron, that electron experiences the full charge of the positive nucleus. In this case, the effective nuclear charge can be calculated from Coulomb's law.
However, in an atom with many electrons the outer electrons are simultaneously attracted to the positive nucleus and repelled by the negatively charged electrons. The effective nuclear charge on such an electron is given by the following equation:
11/11/2016 Dr. Mohammed H. Said 3 Calculating the effective nuclear charge Zeff = Z − S where Z is the number of protons in the nucleus (atomic number), and S is the average number of electrons between the nucleus and the electron in question (the number of nonvalence electrons). S can be found by the systematic application of various rule sets, the simplest of which is known as "Slater's rules" (named after John C. Slater).
11/11/2016 Dr. Mohammed H. Said 4 Shielding
Z* => effective nuclear charge
Z* = Z - S
S => shielding as defined by Slater’s Rules
11/11/2016 Dr. Mohammed H. Said 31 Slater's Rules for Calculating Shielding 1. for [ns, np] electrons (e-s), e-s to the right in the modified electronic configuration contribute nothing 2. for [ns, np] e-s, other electrons of same group contribute 0.35 each (except 1s, 0.3) 3. each electron in n - 1 group, contribute 0.85 4. each electron in n - 2 group, contribute 1.0 5. nd & nf group, rules 1 & 2 remain the same, all electrons to the left contribute 1.0 modified electronic configuration [1s][2s2p][3s3p][3d][4s] etc
11/11/2016 Dr. Mohammed H. Said 6 Examples: for the 4 s electron in Cu atom [1s2][2s22p6][3s23p6][3d10][4s1] n - 2 group => 10 * 1.0 n - 1 group => 18 * 0.85 n group => 0 * 0.35
Z* = 29 - ((10 * 1.0) + (18 * 0.85) + (0 * 0.35)) = 29 - 10 - 15.3 = 3.7
11/11/2016 Dr. Mohammed H. Said 7 Example: for a 3 d electron in Cu atom [1s2][2s22p6][3s23p6][3d10][4s1] rule 5. group 18 * 1.0 9 other d electrons * 0.35
Z* = 29 - ((18 * 1.0) + (9 * 0.35)) = 29 - 18 - 3.2 = 7.8
11/11/2016 Dr. Mohammed H. Said 8 Effective Nuclear Charge Effective Nuclear Charge Name Z n-2 n-1 n Z* hydrogen 1 1 helium 2 1 1.7 lithium 3 2 1.3 beryllium 4 2 1 1.95 boron 5 2 2 2.6 carbon 6 2 3 3.25 nitrogen 7 2 4 3.9 oxygen 8 2 5 4.55 fluorine 9 2 6 5.2 neon 10 2 7 5.85 sodium 11 2 8 2.2 magnesium 12 2 8 1 2.85 aluminum 13 2 8 2 3.5 silicon 14 2 8 3 4.15 phosphorus 15 2 8 4 4.8 sulfur 16 2 8 5 5.45 chlorine 17 2 8 6 6.1 argon 18 2 8 7 6.75 potassium 19 10 8 2.2 calcium 20 10 8 1 2.85 scandium 21 10 9 1 3 titanium 22 10 10 1 3.15 vanadium 23 10 11 1 3.3 chromium 24 10 13 2.95 manganese 25 10 13 1 3.6 iron 26 10 14 1 3.75 cobalt 27 10 15 1 3.9 nickel 28 10 16 1 4.05 copper 29 10 18 3.7 zinc 30 10 18 1 4.35 gallium 31 10 18 2 5 germanium 32 10 18 3 5.65
11/11/2016 Dr. Mohammed H. Said 9 11/11/2016 Dr. Mohammed H. Said 10 Atomic Radius • decrease left to right across a period – as nuclear charge increases, number of electrons increase; however, the nucleus acts as a unit charge while the electrons act independently, pulling electrons towards the nucleus, decreasing size • increase top to bottom down a group – each additional electron “shell” shields the outer electrons from the nuclear charge • increases from upper right corner to the lower left corner
11/11/2016 Dr. Mohammed H. Said 11 11/11/2016 Dr. Mohammed H. Said 12 Elemental Properties vs. Atomic Number 9
8
7
6
5 Z*
4
3 a. radius
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 Atomic Number
11/11/2016 Dr. Mohammed H. Said 13 Ionic Radius • same trends as for atomic radius • positive ions smaller than atom • negative ions larger than atom Isoelectronic Series • series of negative ions, noble gas atom, and positive ions with the same electronic confiuration • size decreases as “positive charge” of the nucleus increases
11/11/2016 Dr. Mohammed H. Said 14 Ionization Energy • energy necessary to remove an electron to form a positive ion, I • low value for metals, electrons easily removed • high value for non-metals, electrons difficult to remove • increases from lower left corner of periodic table to the upper right corner
11/11/2016 Dr. Mohammed H. Said 15 Ionization Energies first ionization energy • energy to remove first electron from an atom second ionization energy • energy to remove second electron from a +1 ion etc.
11/11/2016 Dr. Mohammed H. Said 16 Elemental Properties vs. Atomic Number 30
25
20
Z* 15 1st I. E.
10
5
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 Atomic Number
11/11/2016 Dr. Mohammed H. Said 17 Electron Affinity
• energy released when an electron is added to an atom • same trends as ionization energy, increases from lower left corner to the upper right corner
• metals have low “Ea”
• nonmetals have high “Ea”
11/11/2016 Dr. Mohammed H. Said 18 Elemental Properties vs. Atomic Number
30
25
20
15 Z* 1st I. E. E.A. 10
5
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
-5 Atomic Number
11/11/2016 Dr. Mohammed H. Said 19 Electronegativity Pauling Scale • relative attraction of an atom for electrons, its own and those of other atoms • same trends as ionization energy, increases from lower left corner to the upper right corner
• fluorine: E.N. = XP = 4.0 • based on the energetics of bond formation
11/11/2016 Dr. Mohammed H. Said 20 Electronegativity Milliken Scale • Based on the average of the ionization energy and electron affinity
• XM = ½(I + Ea )
11/11/2016 Dr. Mohammed H. Said 21 11/11/2016 Dr. Mohammed H. Said 22