Chem 14A

1
Chem 14A

• July 2, 2007

2
Lecture Outline

• Quantum Numbers
• Orbitals
• Electron Configuration
• Filling Orbital Shells with Electrons
• Atomic Structure
• Periodicity Trends

3
Quantum Numbers

• Quantum numbers give us information about
  orbitals, the 90 probability zones where
  electrons are located
• There are four quantum numbers, each describing
  different aspects of an orbital

4
Quantum Numbers

• Four quantum numbers n,l,ml,ms
• nprinciple quantum number
• n1,2,3, integral values
• Tells us orbital size and energy
• Coefficient value before orbital 1s

5
Quantum Numbers

• l angular momentum quantum number
• l 0,1,(n-1)
• Describes the angular momentum of an electron in
  an orbital
• l value gives the shape of an orbital
• l0 spherical s orbital
• l1 dumbbell p orbital

6
Quantum Numbers

• The number of orbitals per
• subshell increases with increasing l value

7
Quantum Numbers

• ml magnetic quantum number
• ml -l...0l
• Gives spatial orientation of orbital, with one
  value per orbital (ie px,py,pz) found in the
  subshell
• Orbital orientation denoted by Cartesian plane
  coordinates, ie ml1/-1 2px

8
Quantum Numbers

• ms electron spin quantum number 1/2 or -1/2
• Electrons can spin either clockwise or
  counterclockwise
• Clockwise spin produces a magnetic field pointing
  upward by the right-hand rule and is denoted 1/2
  spin-up
• Counterclockwise spin produces a magnetic field
  pointing downward by the right-hand rule and is
  denoted -1/2 spin-down

9
Quantum Numbers

• How do we use quantum numbers to identify an
  orbital?
• n value is orbital coefficient 3dz2
• l value is orbital type

10
Quantum Numbers

• ml value gives possible Cartesian plane
  coordinates
• ml03dz2
• ms value gives electron spin 1/2 or -1/2

11
Quantum Numbers

• Solving a quantum number problem
• Which of following sets of quantum numbers do not
  correspond to an allowed orbital?
• n2, l1, ml-1
• n1, l1, ml0
• n3, l2, ml2

12
Quantum Numbers

• Set 1 gives an allowed orbital of 2p
• Set 2 is not allowed since the maximum l value
  for the set is n-10
• Set 3 gives an allowed orbital of 3d

13
Quick Exercise I.

• Which of the following sets of quantum numbers
  represents an allowed orbital?
• 1. n1, l0, ml2
• 2. n1, l0, ml0
• 3. n2, l-2, ml1
• What set of n and l values define the orbital 4f?

14
Answers to Quick Exercise I.

• 1. n1, l0, ml2 forbidden, ml gt l
• 2. n1, l0, ml0 allowed 1s
• 3. n2, l-2, ml1 forbidden, l must be 0
• 4f orbital n4, l3, (ml -3.3)

15
Review of the Nucleus

• Nucleus of the atom contains protons() and
  neutrons
• Electrons(-) are found outside of the nucleus in
  orbitals, holding the atom together through
  charge attraction to the proton core
• Both core electrons and valence electrons are
  present
• Core electrons are closer to the nucleus and are
  not normally involved in chemical reactions
• Valence electrons are located on the outer
  surface of the atom and participate in chemical
  reactions

16
Orbitals

• Orbital drawings are mathematical representations
  of the probability space where an electron is
  located- not tangible objects
• Orbitals contain nodal planes, or places of zero
  probability
• Degenerate orbitals have the same energy value,
  for example 2px,2py,2pz are degenerate orbitals

17
Orbitals

• Each orbital can hold 2 electrons, therefore
• s orbital 2 electrons
• p orbital set 3 orbitals 6 electrons
• d orbital set 5 orbitals 10 electrons
• f orbital set 7 orbitals 14 electrons
• g orbital set 9 orbitals 18 electrons

18
s orbital with nodes
19
Orbital Shapes

• 3D s orbital

20
p orbitals
21
Orbital Shapes
22
d orbitals
23
Orbital Shapes
24
f orbital shapes
25
f orbitals
26
Electron Configuration Filling orbitals with
Electrons

• Each orbital can hold up to two electrons
• Rules for filling orbitals
• Pauli exclusion principle each electron must
  have a unique set of the four quantum numbers
  (different ms values)
• Aufbau principle electrons are added one by one
  starting with the lowest energy orbital
• Hunds Rule electrons are initially added one by
  one to each subshell, then paired if necessary

27
Electron Configuration Filling orbitals with
Electrons

• Pauli exclusion principle example
• n1, l0, ml0 allowed 1s orbital
• electron 1 n1, l0, ml0, ms 1/2
• electron 2 n1, l0, ml0, ms -1/2

28
Electron Configuration Filling orbitals with
Electrons

• Aufbau principle example

29
Electron Configuration Filling orbitals with
Electrons

• Hunds rule example Fill degenerate orbitals
  with single electrons first, then pair up if
  necessary

30
Electron Configuration Filling orbitals with
Electrons

• For the first three rows of the periodic table,
  the order of orbital filling is
• s p d f for each value of n
• Electron configurations for the transition
  metals, lanthanides and actinides d and f
  subshells are filled before the p subshells
• Two anomalies exist Cr 4s13d5 and Cu 4s1 3d10
• Subshells that are either exactly half-full or
  completely full are more stable than those that
  are partially full

31
Electron Configuration Filling orbitals with
Electrons
32
Electron Configuration Filling orbitals with
Electrons
33
Electron Configuration Filling orbitals with
Electrons
34
Electron Configuration Filling orbitals with
Electrons

• Electrons are filled in order or orbital energy
  level, from lowest to highest

• 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s

35
Electron Configuration Filling orbitals with
Electrons

• When an electronic transition takes place, an
  electron moves from the ground state to a higher
  energy excited state
• Electron configuration of the excited state will
  show this electron promotion into the next energy
  level

36
Quick Exercise II.

• Identify the following elements
• 1. Ne3s23p4
• 2. excited state configuration
  1s22s22p53s1
• 3. ground-state configuration contains 3 unpaired
  6p electrons

37
Answers to Quick Exercise II.

• 1. S
• 2. Ne
• 3. Bi

38
Periodicity

• The periodic table contains elements grouped by
  their chemical similarities
• In general as we move from left to right across
  the periodic table rows, the atomic radius size
  decreases
• Moving down a column of the periodic table brings
  an increase in atomic radius

39
Periodicity

• Alkali Metals first column
• Alkaline Earth Metals second column
• Transition Metals columns 3-12
• Metals columns 3-6 below metalloid area
• Non Metals columns 4-16 excluding metalloids
• Metalloids diagonal elements from Boron to lead
  (approximate)
• Halogens column 7
• Noble gases column 8
• Lanthanides and Actinides last rows

40
Periodicity

• Two important properties related to periodicity
  are ionization energy and electron affinity
• Ionization energy The energy required to remove
  an electron from a gaseous atom or ion

41
Periodicity

• Ionization energy tends to be lowest for the
  alkaline and earth alkali metals, and increases
  across the period to the noble gases
• The ionization energy of an electron is
  proportionate to the energy level of the orbital
  it was removed from

42
Periodicity

• Why does the ionization energy increase across a
  period?
• Shielding core electrons at varying distances
  from the nucleus will shield the valence
  electrons from an increase in positive charge of
  the nucleus, allowing the valence electrons to be
  removed more easily

43
Periodicity

• However, as we move across a period, the nuclear
  charge () increases. Across a period, the
  electrons are all roughly the same distance away
  from the nucleus
• Since the electrons are all about the same
  distance away from the nucleus, they will not be
  able to shield each other from the increasing
  positive charge very well, and the ionization
  energy increases as we go across the period

44
Periodicity

• Shielding makes it easier to remove valence
  electrons because the core electrons effectively
  minimize the amount of charge the valence
  electrons experience, due to inter-electron
  repulsion
• This phenomenon is termed effective nuclear
  charge, Zeff, and is always lower than the actual
  nuclear charge

45
Periodicity

• Electrons are removed in a stepwise fashion
• 1st ionization energyremoving the first electron
  from the highest energy orbital
• 2nd ionization energyremoving the second
  electron
• After one electron is removed, it becomes much
  more difficult to remove subsequent electrons, so
  the 2nd ionization energy value is usually much
  higher than the first

46
Quick Exercise III.

• The first ionization energy of phosphorus is 1060
  kJ/mole, and that for sulfur is 1005 kJ/mole.
  Why?
• (Phosphorus has a valence configuration of
  3s23p3 and sulfur has a valence configuration of
  3s23p4)

47
Answers to Quick Exercise III.

• Although phosphorus comes just before sulfur on
  the periodic table, it has a slightly higher
  ionization energy because removing an electron
  from a half-filled (or completely filled)
  subshell is more difficult than removing an
  electron from a partially filled subshell

48
Periodicity

• Electron affinity is another important property
  related to periodicity
• Electron Affinity The change in energy
  associated with the addition of an electron to a
  gaseous atom, forming an anion
• Anion negatively charged ion
• Cation positively charged ion

49
Periodicity

• Electron Affinity values in general increase
  across a period when moving from left to right
• This means that the halides give off a greater
  quantity of energy when they form anions versus
  elements on the left, such as the alkali metals,
  indicating that these anions are more
  energetically favorable
• Electron affinity tend to decrease when going
  down a row in the periodic table, but there are
  numerous exceptions