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Lecture 6. Multiple electron systems and Atomic Orbitals 1.12-1.17 3-Sept. Assigned HW Due: Monday 6-Sept. Review 1.7-1.11. 3 quantum numbers completely describe an atomic orbital n  Principle Quantum Number O nly variable calculating energy ONLY for one electron systems!

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lecture 6
Lecture 6

Multiple electron systems and Atomic Orbitals

1.12-1.17

3-Sept.

Assigned HW

Due: Monday 6-Sept

review 1 7 1 11
Review 1.7-1.11
  • 3 quantum numbers completely describe an atomic orbital
    • n  Principle Quantum Number
      • Only variable calculating energy ONLY for one electron systems!
    • l  Orbital Quantum Number 0  n-1
      • deals with the radial component , R(r), of the wavefunction
      • Determines the 2D shape of an atomic orbital.
    • ml  Magnetic Quantum Number -l l
      • Angular component, Y(θ, Φ), of wavefunction
      • 3D orientation
  • To describe an electron within an atomic orbital, we need one more quantum number
    • ms  Spin Quantum Number
  • Orbitals have phases, which are determined by the (+) or (-) regions of R(r)
    • ‘lobes’ alternate in phase
  • In all cases, there are n nodes for an atomic orbital.
let s review this
Let’s Review This
  • List all the possible sets of quantum number for an electron in a 2p orbital
  • How many different 2p-orbitals are there?
  • How does the energy differ between these orbitals?

n

l

ml

ms

multi electron systems
Multi-electron Systems
  • What happens when we don’t have a hydrogen atom?
  • How will these differences influence the attractive energy that an electron feels from the nucleus?

1

2

9

0

2

10

1

2

9

multi electron energies
Multi-electron Energies
  • Energy contributions to multiple electron systems
    • Attraction between the nucleus and the 1st electron
    • Attraction between the nucleus and the 2nd electron
    • Repulsion between 1st electron and 2nd electron

r1

r2

Why is there a factor of Z in the terms that include the nucleus?

Why are attractive energies (-) and repulsions (+)?

r3

multi electron energies shielding
Multi-electron Energies - Shielding
  • Consider Li.
    • Z = ___
  • As we fill in the electrons, not all have the same energy!
    • 1st electron feels NO repulsion because there are no other electrons
    • 2nd electron feels a repulsion from the 1st electron
    • 3rd electron feels repulsion from both of these electron.

r1

+3

+3

+3

r2

r3

r4

r5 and r6

shielding and effective nuclear charge
Shielding and Effective Nuclear Charge
  • This decreased stabilization (increased energy) resulting from adding additional electrons is termed shielding.
    • Adding electrons around an atom’s nucleus minimizes the potential stabilizing energy that the next electron can feel.
  • Effective Nuclear Charge (Zeff)

Other electrons

r

shielding and shell energy
Shielding and Shell Energy
  • We saw in the hydrogen atom that as n increases, the energy increases or decreases?

E

  • Same is true for multiple electron atoms

n =

n =

n =

shielding and orbital energies
Shielding and Orbital Energies
  • Electron shielding results in a shift in the stabilizing energy associated with orbitals within the same shell
    • Consider n = 2.
      • Which orbital do you think should have the lowest energy?
      • Why?
shielding and orbital energies1
Shielding and Orbital Energies

Within a given shell, atomic orbital energies increase with l

s < p < d < f

E

Note that each of these orbitals have a unique set of quantum numbers.

f

Electrons occupy the orbitals according to lowest energy first.

How many electrons can each orbital hold?

d

degenerate

These orbitals are all the same energy

p

s

Which orbital is this?

n = 4, l = 0, ml = 0

shielding and orbital energies2
Shielding and Orbital Energies
  • General scheme  increasing energy of atomic orbitals

The 4s orbital is occupied before the 3d because it has a lower energy. Why might this be?

Hund’s rule

Add Z electrons to the orbitals in the order shown here. Never more than 2 electrons per orbital.

If multiple isoenergeticorbitals are available, add electrons with parallel spins to EACH orbital before adding a 2nd electron to any one orbital.

shielding and orbital energies3
Shielding and Orbital Energies
  • This scheme can also be seen in the periodic table:

Why are the blocks named the way that they are?

What do you think the numbers below each block mean?

filling in atomic orbitals
Filling in Atomic Orbitals

Let’s fill in the electrons of Helium

How many electrons?

Shorthand:

1s2

E

Electrons occupy the orbitals according to lowest energy first.

2s

Helium Ground State

1s

Orbitals can hold 2 electrons!

shielding and orbital energies4
Shielding and Orbital Energies

Let’s fill in the electrons of Helium

How many electrons?

E

Shorthand?

1s12s1

2s

Helium Excited State

1s

shielding and orbital energies5
Shielding and Orbital Energies

Beryllium

How many electrons?

C

Shorthand:

1s22s2

E

2p

2s

1s

shielding and orbital energies6
Shielding and Orbital Energies

C

Shorthand:

1s22s12p1

What would the excited state of Be look like?

E

What happens when it relaxes……?

2p

ENERGY

2s

1s

shielding and orbital energies7
Shielding and Orbital Energies

C

Iron

How many electrons?

Shorthand:

[Ar]4s23d6

E

We’re too lazy to write out ALL the orbitals!

Lazy chemists approach:

Pick an atom that represents the last full shell (this well be a noble gas).

Put it in brackets

Count the number of electrons in the valence shell.

Fill in the valence electrons as we’ve done in the previous examples.

3d

4s

[Ar]

sample problems
Sample Problems

Write the ground state electron configuration for Bismuth.

1st Excited State.

Now Promethium (Z = 61)

periodic trends atomic radius
Periodic Trends – Atomic Radius
  • Atomic Radius is dictated by the number of shells and the charge of the nucleus vs. total charge of electrons.
    • Shell – The atomic radius increases with the shell – so increases and we go DOWN the periodic table
      • Example: The atomic radius of K > Na
    • Within the same shell, we’re adding protons and electrons
    • Shielding is still ~the same, so increasing Z decreases radius
      • Example: The atomic radius of Cl < S < P

General Trend: decreases from left to right and increases down

periodic trends ionic radius
Periodic Trends – Ionic Radius
  • What influence will adding an electron have to the radius of an atom?
    • Have we added any protons?
    • So we have NO additional attraction  radius increases
  • What happens if we remove an electron?
    • Remove repulsive force from electron-electron interactions
    • Remaining electrons feel more (+)  radius decreases
periodic trends ionic radius1
Periodic Trends – Ionic Radius

Same # electrons, so why different size?

periodic trends ionization energy
Periodic Trends – Ionization Energy
  • The amount of energy to remove an electron from an atom.
  • Directly related to the energy of the electron
    • 1st ionization energy < 2nd ionization energy, etc.

0

E

  • Easiest to remember that this value is inversely related to atomic radius
  • When the radius is small, the electron is bound tightly, so high ionization energy

2s

1s

Compare the ionization energy of F to As

periodic trends ionization energy1
Periodic Trends – Ionization Energy

N > O

0

E

2s

There is a special stabilization energy when degenerate energy orbitals are completely full and half full.

1s

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