The Quantum View of the Atom

Vocabulary:

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

“Under the Wave off Kanagawa”,

Katsushika Hokusai, 1829

AP Topics

Topic 1.5: Atomic Structure and Electron Configuration

Learning Objective: Represent the ground-state electron configuration of an element or ions of an element using the Aufbau principle.

Essential Knowledge:

• In atoms and ions, the electrons can be thought of as being in “shells (energy levels)” and “subshells (sublevels),” as described by the ground-state electron configuration. Inner electrons are called core electrons, and outer electrons are called valence electrons. The ground-state electron configuration is explained by quantum mechanics, as delineated in the Aufbau principle and exemplified in the periodic table of the elements.

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.

What was wrong with Bohr’s model?

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

Where’s the love?

Neils Bohr (Denmark)

Nobel prize in Physics, 1922

Heisenberg Uncertainty Principle

Heisenberg Uncertainty Principle: You can not know both the position and the energy of an electron simultaneously.

Werner Heisenberg (Germany)

Nobel prize in Physics, 1932

Let’s watch this:

Click Here to Watch Video

Schrödinger and Probability

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

Erwin Schrödinger

(Austria)

Nobel prize in Physics, 1933

Schrödinger’s Cat

Schrödinger’s Cat

Energy Levels (shell)

• The energy level (shell) that an electron occupies is called the principle quantum number (n).
• n can equal 1, 2, 3, …
• n=1 means the electron is on the 1^st energy level, n=2 means the electron is on the 2^nd energy level, etc.
• This is very similar to Bohr’s model.

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); they are the probable locations of electrons.
• There are 4 types of orbitals: s, p, d, and f.
• Orbitals have various shapes and each energy level has different types of orbitals. (There are n² orbitals per energy level (n)).

1^st Energy Level (n = 1)

On the first energy level there is only one type of subshell (orbital), the s-orbital. We call this the 1s orbital.

s-orbitals are spherical and represent the probable location of an electron. The nucleus is in the middle and the electron is somewhere in the region of the s-orbital.

s- orbital

cross section of s- orbital

1^st Energy Level (n = 1)

cross section of s- orbital

The Nature of Orbitals

The electron’s position in an orbital of an atom can be compared to a spinning airplane propeller. The propeller blade has the same probability of being anywhere in the blurry region, but you cannot tell its location at any instant.

1^st Energy Level (n = 1)

Experimental evidence shows that only 2 electrons can fit into any orbital. That means only 2 electrons can fit in the 1s orbital and therefore on the first energy level (n=1). But if there are 2 electrons in an orbital, each electron has opposite “spin” (magnetic field). This concept is called the Pauli Exclusion Principle. The two types of spin are called “positive” spin and “negative” spin (no relation to + and – charge).

Wolfgang Pauli

(Austria):

Nobel prize in Physics, 1945

Example

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

Example

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: in their ground state, 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)

Orbital Diagram

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

Energy

Orbital Diagram

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

Energy

This is called an orbital diagram.

Atoms need more space

The 1^st energy level only has an s-orbital (n² orbitals), and that orbital can only hold 2 electrons. Where do atoms with more than 2 electrons put their electrons?

2^nd Energy Level (n = 2)

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

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2^nd Energy Level (n = 2)

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

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2^nd Energy Level (n = 2)

• Also on the n = 2 level are p orbitals which are slightly higher energy than the 2s orbital.
• 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 2p_x, 2p_y, and 2p_z.

2p orbital

All three of these exist simultaneously and each can hold 2 electrons.

Here’s what all three look like together:

2^nd Energy Level

So if you’re keeping track, that means that on the second energy level, there are 4 orbitals (n² orbitals): the 2s, 2p_x, 2p_y, and 2p_z.

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

Here’s what we’ve got so far:

2^nd Energy Level

So if you’re keeping track, that means that on the second energy level, there are 4 orbitals (n² orbitals): the 2s, 2p_x, 2p_y, and 2p_z.

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

Here’s what we’ve got so far:

1s

2^nd Energy Level

So if you’re keeping track, that means that on the second energy level, there are 4 orbitals (n² orbitals): the 2s, 2p_x, 2p_y, and 2p_z.

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

Here’s what we’ve got so far:

1s, 2s

2^nd Energy Level

So if you’re keeping track, that means that on the second energy level, there are 4 orbitals (n² orbitals): the 2s, 2p_x, 2p_y, and 2p_z.

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

Here’s what we’ve got so far:

1s, 2s, 2p_x

2^nd Energy Level

So if you’re keeping track, that means that on the second energy level, there are 4 orbitals (n² orbitals): the 2s, 2p_x, 2p_y, and 2p_z.

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

Here’s what we’ve got so far:

1s, 2s, 2p_x, 2p_y

2^nd Energy Level

So if you’re keeping track, that means that on the second energy level, there are 4 orbitals (n² orbitals): the 2s, 2p_x, 2p_y, and 2p_z.

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

Here’s what we’ve got so far:

1s, 2s, 2p_x, 2p_y, 2p_z

2^nd Energy Level

This is getting a little messy, right?

So:

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!

Example

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

Orbital Diagram

First, fill the lowest energy level first...the 1s orbital.

Energy

Orbital Diagram

First, fill the lowest energy level first...the 1s orbital.

Energy

Orbital Diagram

Next, move to the n=2 level and fill the 2s orbital.

Energy

Orbital Diagram

Next, move to the n=2 level and fill the 2s orbital.

​

Energy

Orbital Diagram

Finally, place the last electron in one of the 2p orbitals.

Energy

There are three lines for the p orbitals because there are three types of p orbitals (p_x, p_y, and p_z).

Orbital Diagram

Finally, place the last electron in one of the 2p orbitals.

Energy

Electron Configuration

This can be written more concisely as an electron configuration (a shorthand way of representing the locations of electrons in an atom): 1s²2s²2p¹

Energy

Example 2

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

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.

​

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

Example 2

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

Energy

Example 2

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

Energy

Example 2

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

Energy

Example 2

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

Energy

Example 2

The first 4 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?

Energy

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 with “parallel” spin (the same spin) in order minimize repulsion. Remaining electrons then pair up with them. This is called Hund’s Rule.

Energy

Friedrich Hund (German)

Orbitals with the same energy are called “degenerate orbitals”

Example 2

Example 2

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

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Energy

Example 2

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

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Energy

Example 2

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

​

Energy

Example 2

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

​

Energy

Example 2

And what is the electron configuration?

​

Energy

Example 2

And what is the electron configuration?

1s²2s²2p³

Energy

2^nd Energy Level

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

Energy

2^nd Energy Level.

What if an atom needs more room for electrons?

Energy

3^rd Energy Level (n = 3)

On the third energy level there are three types of orbitals and a total of 9 orbitals (n² 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:

Types of orbitals

• The d-orbitals (all together)

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.

3^rd Energy Level

So far:

4^th 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:

4^th Energy Level

So far:

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.

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

Summary

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

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Energy

Summary

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

Orbital Diagrams

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

Orbital Diagrams

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

16 electrons (because its atomic number is 16)

Orbital Diagrams

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

Orbital Diagrams

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

Orbital Diagrams

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

Orbital Diagrams

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

Orbital Diagrams

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

Orbital Diagrams

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

Orbital Diagrams

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

Orbital Diagrams

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

Orbital Diagrams

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

That’s it! And the electron configuration?

​

Orbital Diagrams

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

That’s it! And the electron configuration?

1s²2s²2p⁶3s²3p⁴

Orbital Diagrams

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

Orbital Diagrams

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

Orbital Diagrams

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

Orbital Diagrams

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

Orbital Diagrams

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

Orbital Diagrams

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

Orbital Diagrams

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

Orbital Diagrams

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

Orbital Diagrams

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

Orbital Diagrams

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

Orbital Diagrams

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

Orbital Diagrams

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

Orbital Diagrams

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

And the electron configuration?

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 the S^2- ion.

Orbital Diagrams

Try one on your own: draw the orbital diagram and electron configuration for the S^2- ion.

And the electron configuration?

1s²2s²2p⁶3s²3p⁶

Orbital Diagrams

What neutral atom has the same electron configuration as S^2-?

And the electron configuration?

1s²2s²2p⁶3s²3p⁶

Orbital Diagrams

Argon! Because S^2- and Ar have the same electron configuration, we say they are isoelectric.

And the electron configuration?

1s²2s²2p⁶3s²3p⁶