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Relative Energies of Atomic Orbitals

One-Electron Species

  • For a one-electron species like the hydrogen atom, there is no electron-electron repulsion. Therefore, all the subshells of the same n are degenerate.
  • Orbitals at the same energy level are called degenerate.




Wize Tip
It will be helpful to understand the difference between a shell, a subshell, and an orbital.
We will label these in the diagram above!

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Multi-Electron Species

  • With multi-electron species, there are interactions between electrons (electron-electron repulsion)
  • The energy level diagram of the orbitals looks like this:



Wize Concept
  • S subshells hold a maximum of
    2
    electrons
  • P subshells hold a maximum of
    6
    electrons
  • D subshells hold a maximum of
    10
    electrons
  • F subshells hold a maximum of
    14
    electrons


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The total number of orbitals in a given shell is given by:n2\boxed{\text{The total number of orbitals in a given shell is given by}: n^2}

Example:

If n=2, what is the total number of orbitals in that shell?
  • 22=4
    , circle the
    4
    orbitals that have n=2 above

What if we wanted to know the maximum number of electrons we could have if n=2?

  • We already found that total number of orbitals for this shell (
    4
    )
  • What is the maximum number of electrons we could have in each orbital?
    2
  • Therefore the maximum number of electrons possible when n=2 is
    8

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Rules for Orbital Filling

1) Aufbau Principle

Electrons will always occupy the lowest available energy level first.



Watch Out!
Memorize the order of orbital filling (or just familiarize yourself enough with the periodic table to know the order!): 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p...

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2) Hund’s Rule

Due to electron-electron repulsion, electrons will fill orbitals of the same energy singly before pairing up

Electrons don't want to be next to each other unless they have to be!
Example: Fill out the following orbital diagram for C


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3) Pauli Exclusion Principle

No two electrons in an atom will have the same set of 4 quantum numbers.


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Example: Orbital Filling Diagrams

Draw the orbital diagram for oxygen.


1s2s2p\begin{array}{ccccc}\boxed{\upharpoonleft\downharpoonright}&\boxed{\upharpoonleft\downharpoonright}&\boxed{\upharpoonleft\downharpoonright}\boxed{\upharpoonleft}\boxed{\upharpoonleft}\\ 1s&2s&2p\end{array}

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Example: Orbital Filling Diagrams

Complete the atomic orbital diagram below for a neutral calcium atom.

Practice: Orbital Filling Diagrams

Which of the orbital diagrams gives the correct electron configuration for an atom of boron, in the ground state?

Practice: Number of Orbitals

How many different atomic orbitals exist where n = 3?