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The Quantum Model, Orbitals, and Electron Configurations

Vocabulary:

  1. Heisenberg Uncertainty Principle
  2. probability wave
  3. orbital (subshell)
  4. shell (energy level)
  5. s, p, d, and f
  6. Pauli Exclusion Principle
  7. spin
  8. Aufbau Principle
  9. Orbital Diagram
  10. Electron Configurations

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“The Great Wave off Kanagawa”,

Katsushika Hokusai, 1829

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Things were going along just fine in particle physics, and then…

Bohr’s atom explained a lot, but more and more evidence was pointing to some problems.

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What was wrong with Bohr’s model?

  • Only worked for hydrogen
  • Violated Heisenberg’s uncertainty principle

Where’s the love?

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Heisenberg Uncertainty Principle

  • You can not know both the position and the energy of an electron simultaneously.

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Schrödinger and Probability

  • Erwin Schrödinger solved the problem by developing “probability waves” using his wave equation.
  • Probability wave: given an electron’s energy, Schrödinger's wave equations identify the probable location of that electron.

I hope no one asks me to explain that!

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Energy Levels (shell), n

  • According to Schrödinger, Electrons still exist in energy levels (n) like Bohr discovered
  • n can equal 1, 2, 3, …
  • n=1 means the electron is on the 1st energy level, n=2 means the electron is on the 2nd energy level, etc.

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Orbitals (subshells)

  • We represent probability waves as graphs of the probable location of an electron in its ground state around the nucleus of an atom.
  • These graphs are interpreted as orbitals (also called subshells) and are the probable locations of electrons.
  • Orbitals have various shapes and each energy level has different types of orbitals.
  • There are 4 types of orbitals: s, p, d, and f.

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1st Energy Level (n = 1)

  • Only one type of orbital on n=1, the s-orbital.
  • Called the “1s” orbital.
  • s-orbitals are spherical and represent the probable location of an electron with the nucleus in the middle.

s- orbital

cross section of s- orbital

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Pauli Exclusion Principle

  • Only 2 electrons can fit into any orbital.
  • That means only 2 electrons can fit in the 1s orbital
  • If there are 2 electrons in an orbital, each electron has opposite “spin” (magnetic field).

Wolfgang Pauli

(Austria):

Nobel prize in Physics, 1945

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Example

Where do the 2 electrons of helium reside in the atom?

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Orbital Diagram

Where do the 2 electrons of helium reside in the atom?

We’re going to draw an orbital diagram.

To answer this, we’re going lay down some rules:

  1. Use arrows to represent electrons: ↑ for electron with positive spin and ↓ for electron with negative spin.
  2. Use labelled lines to represent orbitals. (ex. 1s ____ )
  3. Electrons must be in lowest energy levels possible (this is called the Aufbau Principle: electrons fill lowest energy levels first and then fill up to higher energy levels)
  4. Only two electrons can occupy any one orbital (the Pauli Exclusion Principle)

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Orbital Diagram

Where do the 2 electrons of helium reside in the atom?

Energy

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Orbital Diagram

Where do the 2 electrons of helium reside in the atom?

Energy

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Atoms need more space

The 1st energy level only has an s-orbital, and that orbital can only hold 2 electrons.

Where do atoms with more than 2 electrons put their electrons?

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2nd Energy Level (n = 2)

The 1st energy level still exists, but around it is the larger 2s orbital.

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2nd Energy Level (n = 2)

The 1s and 2s orbitals are shown below overlapping.

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2nd Energy Level (n = 2)

  • Also on the n = 2 level are p orbitals.
  • While there is only one type of s-orbital (a sphere), there 3 different types of p-orbitals.
  • Each p-orbital looks the same (“dumbbell shape”) but each is along a different axis. They are called 2px, 2py, and 2pz.

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2p orbital

  • All three of these exist simultaneously and each can hold 2 electrons.
  • Here’s what all three look like together:

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2nd Energy Level

So if you’re keeping track, that means that on the second energy level, there are 4 orbital:

    • 2s
    • 2px
    • 2py
    • 2pz.

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That means that 8 total electrons can exist on the 2nd energy level.

Here’s what we’ve got so far:

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2nd Energy Level

So if you’re keeping track, that means that on the second energy level, there are 4 orbital:

    • 2s
    • 2px
    • 2py
    • 2pz.

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That means that 8 total electrons can exist on the 2nd energy level.

Here’s what we’ve got so far:

1s

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2nd Energy Level

So if you’re keeping track, that means that on the second energy level, there are 4 orbital:

    • 2s
    • 2px
    • 2py
    • 2pz.

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That means that 8 total electrons can exist on the 2nd energy level.

Here’s what we’ve got so far:

1s, 2s

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2nd Energy Level

So if you’re keeping track, that means that on the second energy level, there are 4 orbital:

    • 2s
    • 2px
    • 2py
    • 2pz.

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That means that 8 total electrons can exist on the 2nd energy level.

Here’s what we’ve got so far:

1s, 2s, 2px

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2nd Energy Level

So if you’re keeping track, that means that on the second energy level, there are 4 orbital:

    • 2s
    • 2px
    • 2py
    • 2pz.

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That means that 8 total electrons can exist on the 2nd energy level.

Here’s what we’ve got so far:

1s, 2s, 2px, 2py

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2nd Energy Level

So if you’re keeping track, that means that on the second energy level, there are 4 orbital:

    • 2s
    • 2px
    • 2py
    • 2pz.

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That means that 8 total electrons can exist on the 2nd energy level.

Here’s what we’ve got so far:

1s, 2s, 2px, 2py, 2pz

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Let’s see how this applies so far

  • As atoms get bigger, they have more and more electrons.
  • How do we know where all those electrons go?
  • The orbital diagrams and electron filling rules from earlier!

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Example

Where do the 5 electrons of boron reside in the atom?

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Orbital Diagram

Where do the 5 electrons of boron reside in the atom?

Energy

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Orbital Diagram

Where do the 5 electrons of boron reside in the atom?

Energy

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Orbital Diagram

Where do the 5 electrons of boron reside in the atom?

Energy

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Orbital Diagram

Where do the 5 electrons of boron reside in the atom?

Energy

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Orbital Diagram

Where do the 5 electrons of boron reside in the atom?

Energy

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Orbital Diagram

Where do the 5 electrons of boron reside in the atom?

Energy

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Electron Configuration

This can be written more concisely as an electron configuration: 1s22s22p1

Energy

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Example 2

Example 2: Write the orbital diagram and the electron configuration for nitrogen.

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Example 2

Example 2: Write the orbital diagram and the electron configuration for nitrogen.

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First, we need to determine how many electron nitrogen has. Look at your periodic table.

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Example 2

Example 2: Write the orbital diagram and the electron configuration for nitrogen.

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First, we need to determine how many electron nitrogen has. Look at your periodic table.

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Nitrogen has an atomic number of 7, so it has 7 electrons.

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Example 2

Now start placing those 7 electron in their lowest energy levels.

Energy

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Example 2

Now start placing those 7 electron in their lowest energy levels.

Energy

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Example 2

Now start placing those 7 electron in their lowest energy levels.

Energy

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Example 2

Now start placing those 7 electron in their lowest energy levels.

Energy

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Example 2

  • The first 4 electrons were easy. But we still have 3 more to go.
  • Where should they go?
  • Think about the charge of electrons. Do you think they will be close together or far apart in the 2p orbitals?

Energy

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Example 2

Hopefully you said far apart. If electrons are filling orbitals with the same energy (like the three 2p orbitals), they go in one at a time in order minimize repulsion. They then pair up if they must. This is called Hund’s Rule.

Energy

Friedrich Hund (German)

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Example 2

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Example 2

So here is the final orbital diagram for the 7 electrons of nitrogen:

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Energy

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Example 2

So here is the final orbital diagram for the 7 electrons of nitrogen:

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Energy

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Example 2

So here is the final orbital diagram for the 7 electrons of nitrogen:

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Energy

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Example 2

So here is the final orbital diagram for the 7 electrons of nitrogen:

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Energy

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Example 2

And what is the electron configuration?

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Energy

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Example 2

And what is the electron configuration?

1s22s22p3

Energy

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2nd Energy Level

Notice that only 8 electrons can fit on the 2nd energy level. (What element would this be?)

Energy

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2nd Energy Level.

What if an atom needs more room for electrons?

Energy

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3rd Energy Level (n = 3)

On the third energy level there three types of orbitals:

  • 1 larger s-orbital,
  • 3 larger p-orbitals, and
  • 5 d-orbitals.

These are called the 3s orbitals, the 3p orbitals, and the 3d orbitals.

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d-orbitals

Here’s what the five d-orbitals look like:

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Types of orbitals

  • The d-orbitals (all together)

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All together

You can imagine trying to draw ALL of the orbitals on each energy level so far would make a giant mess, so we’re not going to.

But remember, all of these orbitals exist at the same time.

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4th Energy Level (n = 4)

On the fourth energy level there four types of orbitals:

  • 1 larger s-orbital,
  • 3 larger p-orbitals,
  • 5 larger d-orbitals, and
  • 7 f-orbitals

These are called the 4s orbitals, the 4p orbitals, the 4d orbitals, and the 4f orbitals.

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f-orbitals

Here’s what the seven f-orbitals look like:

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Sigh of relief

  • There are no more practical types of orbitals at this point.
  • There are 3 more energy levels (n=5, n=6, and n=7) but there are only s, p, d, and f orbitals on each.
  • No atom has enough electrons to go to the next type of orbital, the g-orbital.

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For those that are curious… here are the nine g-orbitals.

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Summary

Here are the energy levels and the orbitals that can exist on each:

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Energy

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Summary

The specific order of the energies can be seen in the following chart (copy it!):

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Orbital Diagrams

Let’s practice: Draw the orbital diagram for sulfur (how many electrons?)

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Orbital Diagrams

Let’s practice: Draw the orbital diagram for sulfur (how many electrons?)

16 electrons (because its atomic number is 16)

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Orbital Diagrams

Let’s practice: Draw the orbital diagram for sulfur: 16 electrons.

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Orbital Diagrams

Let’s practice: Draw the orbital diagram for sulfur: 16 electrons.

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Orbital Diagrams

Let’s practice: Draw the orbital diagram for sulfur : 16 electrons.

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Orbital Diagrams

Let’s practice: Draw the orbital diagram for sulfur : 16 electrons.

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Orbital Diagrams

Let’s practice: Draw the orbital diagram for sulfur : 16 electrons.

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Orbital Diagrams

Let’s practice: Draw the orbital diagram for sulfur : 16 electrons.

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Orbital Diagrams

Let’s practice: Draw the orbital diagram for sulfur : 16 electrons.

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Orbital Diagrams

Let’s practice: Draw the orbital diagram for sulfur : 16 electrons.

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Orbital Diagrams

Let’s practice: Draw the orbital diagram for sulfur : 16 electrons.

That’s it! And the electron configuration?

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Orbital Diagrams

Let’s practice: Draw the orbital diagram for sulfur : 16 electrons.

That’s it! And the electron configuration?

1s22s22p63s23p4

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Orbital Diagrams

Another one: Draw the orbital diagram for molybdenum: 42 electrons.

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Orbital Diagrams

Another one: Draw the orbital diagram for molybdenum: 42 electrons.

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Orbital Diagrams

Another one: Draw the orbital diagram for molybdenum: 42 electrons.

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Orbital Diagrams

Another one: Draw the orbital diagram for molybdenum: 42 electrons.

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Orbital Diagrams

Another one: Draw the orbital diagram for molybdenum: 42 electrons.

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Orbital Diagrams

Another one: Draw the orbital diagram for molybdenum: 42 electrons.

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Orbital Diagrams

Another one: Draw the orbital diagram for molybdenum: 42 electrons.

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Orbital Diagrams

Another one: Draw the orbital diagram for molybdenum: 42 electrons.

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Orbital Diagrams

Another one: Draw the orbital diagram for molybdenum: 42 electrons.

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Orbital Diagrams

Another one: Draw the orbital diagram for molybdenum: 42 electrons.

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Orbital Diagrams

Another one: Draw the orbital diagram for molybdenum: 42 electrons.

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Orbital Diagrams

Another one: Draw the orbital diagram for molybdenum: 42 electrons.

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Orbital Diagrams

Another one: Draw the orbital diagram for molybdenum: 42 electrons.

And the electron configuration?

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Orbital Diagrams

Another one: Draw the orbital diagram for molybdenum: 42 electrons.

And the electron configuration?

1s22s22p63s23p64s23d104p65s24d4

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Orbital Diagrams

Try one on your own: draw the orbital diagram and electron configuration for titanium.

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Orbital Diagrams

Try one on your own: draw the orbital diagram and electron configuration for titanium.

And the electron configuration?

1s22s22p63s23p64s23d2