Quiz 2/ A/ How many orbitals are possible for n=3? B/ How many orbital nodes do 2S ,3P ...€¦ · · 2016-11-12B/ How many orbital nodes do 2S ,3P ,4d and 5f orbitals exhibit?

11/11/2016 Dr. Mohammed H. Said 1

Quiz 2/

A/ How many orbitals are possible for

n=3?

B/ How many orbital nodes do 2S ,3P

,4d and 5f orbitals exhibit?

2lecture 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


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:


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).


Shielding

Z* => effective nuclear charge

Z* = Z - S

S => shielding as defined by Slater’s Rules


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


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


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




Elemental Properties vs. Atomic Number

0

1

2

3

4

5

6

7

8

9

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

Z*

a.radius

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


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


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.




0

5

10

15

20

25

30

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

Z*

1st I. E.


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”



-5

0

5

10

15

20

25

30

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

Z*

1st I. E.

E.A.

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


Electronegativity

Milliken Scale

• Based on the average of the ionization energy

and electron affinity

• XM = ½(I + Ea )



Documents

Quiz 2/ A/ How many orbitals are possible for n=3? B/ How many orbital nodes do 2S ,3P ...€¦ · · 2016-11-12B/ How many orbital nodes do 2S ,3P ,4d and 5f orbitals exhibit?