Quantum Mechanical Model Notes

Electrons DO NOT travel around the nucleus of an atom in orbits like planets around a sun.

Orbitals are 3-D areas around the nucleus with a high probability of finding electrons.

The higher the density of dots indicates the higher (most) probable location(s) of electron(s).

Boundary line = 90% probability of finding electrons within the circular region.

Each electron in an electron cloud has a four-part quantum number. This is like a street address.

Principle Quantum #1 (n): Indicates the relative size and energy of orbitals. It is designated with numbers, 1-7).

Electrons are found at different distances away from the nucleus in different energy levels.

Electrons cannot exist between energy levels (they are like the rungs of a ladder).

Only a certain number of electrons may exist in a given energy level, but the number varies. It can be determined by a formula:

Total number of electrons in level = 2 x (# of energy level )2

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For Example: Energy level 1 = 2 (1)2 = 2 Energy level 2 = 2 (2)2 = 8Solve for the energy levels below using the equation (2 x (# of energy level)2

Energy level 3 = Energy level 4 = Energy levels are broken up into sublevels:

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Principle Quantum #2 (s; p; d; f; etc.): Are called energy sublevels and have specific orbital shapes. Table Team — what is the relationship between n and sublevels?

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Prinicple Quantum Number 3: Designates the orientation of orbitals in the electron cloud.

Principle Quantum Number 4: Designates the ‘spin’ of an electron (either clock-wise or counter clock wise), allowing two electrons to occupy the same orbital.

Each electron has a unique set of four quantum numbers.

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Principle Energy Level 1: Only has one s sublevel (a spherical shape; see model).

A sphere has only one orientation in the space of the electron cloud.

Two electrons may fit in this sublevel—each one has an opposite spin.

Pauli exclusion principle —no more than two electrons may be found in the same orbital.

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An ‘s’ Orbital

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Principle Energy Level 2: Has two energy sublevels: s and p.

There are 2 electrons in a ‘s’ There are 3 different p orbitals, each can hold 2 electrons for 6 total. (‘dumb-bell’ shape; three orientations in electron cloud space).

There can be a total of 8 electrons overall in energy level 2.

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‘p’ Orbitals

Principle Energy Level 3: has 3 sublevels: s, p, and d.

Two electrons in the s orbital

Six total electrons in the three p orbitals.

There are 5 different d orbitals, and 2 electrons can fit in each—for a total of 10.

Total of 18 electrons for energy level 3.

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d-orbital notes

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The five ‘d’ Orbital Images

Principle Energy Level 4: Has 4 sublevels: s, p, d , and f.

2 electrons in s 6 electrons in p10 electrons in d14 electrons in f (7 different orbitals for f)

A total of 32 electrons in this energy level.

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Seven ‘f’ orbitals

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The order that electrons fill up orbitals does not follow the logical order of all 1’s, then all 2’s, then all 3’s, etc.

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The first rule states that each electron occupies the lowest energy level possible. This is called the Aufbau principle.

The second rule for filling orbitals is that only one electron will be put in each orbital of a sublevel until all of them are filled, and after that, they may be paired up until the sublevel is full. This is called Hund’s rule.

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An easy way to remember this is to use the periodic table--it is arranged to show how these orbitals are filled. Stay tuned!

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