Electron Configuration and Atomic Orbitals

1
Electron Configuration and Atomic Orbitals

• Quantum Numbers (section 7.6) Understand what n,
  l and ml are and learn tables 7.1 and 7.2 on p
  308. Be able to specify the values of n, l and
  ml from electron state designations 1s, 2s, 2p,
  etc. and be able to say which values of n, l and
  ml are allowed and which are not allowed.
• Orbital Shapes (section 7.7) Study and be able
  to draw the orbitals in Fig 7.13, 7.14, 7.16 and
  7.17
• Electron Spin and the Pauli Principle (7.8, fig
  7.19) know that electrons have a fourth quantum
  number, ms, that can have the value of 1/2 or
  -1/2
• Polyelectronic Atoms (7.11) Know what is meant
  by a hydrogenic orbital, be able to explain why
  hydrogenic orbitals are used to describe the
  energy states of the electrons in all atoms,
  learn what the aufbau principle is (p 317), learn
  Hund's Rule (p 318), understand fig 7.29 (p 323)
  which shows the filling order of the hydrogenic
  orbitals, learn how to specify electron
  configurations using spectroscopic notation
  (defined in this lecture, e.g. 1s2) and how to
  draw orbital diagrams (p 317-319) to represent
  how electrons in polyelectronic atoms occupy the
  hydrogenic orbitals.

2
Photon Energies are ?E's, Electron Energies are
E's

• Do not forget this!!!!

3
Quantum Numbers

• We have already seen the principle quantum
  number, n, but actually there are two other
  quantum numbers, l and ml
• The value of n limits what l can be. The value
  of l limits what ml can be.
• l can be any integer from 0 to n-1
• ml can be any integer between l and l
• EG/ What are the allowed values of the 3 quantum
  numbers for the n3 and n1 levels of the
  hydrogen atom electron?
• When l 0, called an s state. When l 1,
  called a p state, etc.
• What is the state of l 2 called?

4
Summary of Quantum Numbers
5
Orbital Shapes

• Fig 7.13, 7.14, 7.16, 7.17. Know them, and be
  able to draw them.
• What these figures show is the shape of the
  electron wave in the hydrogen atom. Remember it
  is incorrect to think of the electron as a
  particle moving in a circular orbit. Instead,
  the electron is a 3 dimensional standing wave
  that has a certain shape.

6
Examples of Quantum Numbers

• Which of the following sets of quantum numbers
  are not allowed? (like HW problem 63)
• What then are the allowed states of the
  hydrogen atom? (Ans 1s, 2s, 2p, 3s, 3p, 3d,
  4s, 4p, 4d, 4f...)
• Is the 1p state of hydrogen allowed? If so, why?
  If not, why not?
• Is the 3f state of hydrogen allowed? If so, why?
  If not, why not?

7
Electron Spin and the Pauli Principle

• Electrons are teensy magnets
• They can be pointing up or down.
• Spin is represented by a fourth quantum number,
  ms, which can be either 1/2 (if pointing up) or
  -1/2 (if pointing down).

8
Polyelectronic Atoms and the Aufbau Principle

• What is a hydrogenic orbital or state? The
  hydrogen atom electron's energy states are called
  hydrogenic orbitals
• We use the hydrogenic orbitals (1s, 2s 2p, 3s 3p
  3d, etc.) to describe the energy states of
  electrons in all atoms (even though it is an
  approximation to do so) this is the aufbau
  principle.
• How do we do this? The aufbau principle (in
  operation) has three parts that we need to
  understand the Pauli Principle, Hund's Rule and
  the orbital filling order.

9
The Pauli Principle

• No two electrons on an atom can share the same
  set of quantum numbers (thus every electron has
  to have its own n l ml ms)
• Upshot is spin pairing no more than two
  electrons can share the same orbital, and if two
  electrons share the same orbital, they must have
  opposite spins one is spin up and the other is
  spin down.
• Upshot to make the electron configuration of an
  atom, you add electrons pairwise to the orbitals,
  whenever you can.

10
Hund's Rule

• Said whenever you can on last slide. You can't
  pair electrons when there is an odd number of
  electrons, and Hund's Rule tells us another case
  when they can't when the electrons have a choice
  to occupy separate orbitals alone, then they will
  do that in preference to spin pairing.

11
The Orbital Filling Order (fig 7.29)

• How do we know which orbitals to add the
  electrons to first?
• We add electrons to the orbitals from lowest to
  highest energy
• This figure shows us how to figure out the
  ordering of the energies of the atomic orbitals.
• From this figure, we see that the ordering of the
  energies, from lowest to highest is
• 1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d ... etc

12
Electron Configurations

• Electron configuration how the electrons in a
  polyelectronic atom occupy the hydrogenic
  orbitals.
• The aufbau principle tells us how.
• Armed with the three aspects of the aubau
  principle we can now STATE the aufbau principle.
• Aufbau principle to describe the electronic
  states of a polyelectronic atom, we build up an
  electron configuration for it by adding electrons
  to the hydrogenic orbitals, following the known
  orbital filling order and obeying both Hund's
  Rule and the Pauli Principle

13
Two (of many) Ways of Representing Electron
Configurations

• Spectroscopic notation this is the one you're
  used to probably. In this notation, the electron
  configuration of hydrogen is 1s1, He is 1s2, C is
  1s2 2s12p2 etc.
• Orbital diagrams this notation contains more
  information than spectroscopic notation, because
  it shows the spin state and how the orbitals are
  occupied (as on p 317-319)

14
In-Class Exercise

• Draw the electron configuration of the following
  atoms in both spectroscopic notation and in
  orbital diagrams (like HW problem 73)
• Cl As Sr W Pb