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Quantum MechanicalModel of the Atom

Mathematical laws can identify the regions outside of the nucleus where electrons are most likely to be found.

These laws are beyond the scope of this class…

Heisenberg Uncertainty Principle

The more certain you are about where the electron is, the less certain you can be about where it is going.

The more certain you are about where the electron is going, the less certain you can be about where it is.

“One cannot simultaneously determine both the position and momentum of an electron.”

WernerHeisenberg

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Quantum NumbersEach electron in an atom has a unique set of 4 quantum numbers which describe it.

• Principal quantum number• Angular momentum quantum number• Magnetic quantum number• Spin quantum number

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Pauli Exclusion Principle

Two electrons occupying the same orbital must have opposite spins

Wolfgang Pauli

Assigning the Numbers• The three quantum numbers (n, l, and m) are integers.• The principal quantum number (n) cannot be zero. • n must be 1, 2, 3, etc.• The angular momentum quantum number (l ) can be any integer between 0 and n - 1.• For n = 3, l can be either 0, 1, or 2.• The magnetic quantum number (ml) can be any integer between -l and +l.• For l = 2, m can be either -2, -1, 0, +1, +2.

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In a given atom, no 2 electrons have the same set of 4 quantum numbers.

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Periodic Trends

­ observed trends in several important atomic properties including atomic size, ionization energy and electron affinity.

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Definition: Half of the distance between nuclei in a covalently bonded diatomic molecule

• Radius decreases across a period• Increased effective nuclear charge due to decreased shielding • Radius increases down a group• Each row on the periodic table adds a “shell” or energy level to the atom

Atomic Radius

Table of Atomic Radii

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Periodic Trends

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• Increases for successive electrons taken from the same atom• Tends to increase across a period• Electrons in the same quantum level do not shield as effectively as electrons in inner levels• Irregularities at half filled and filled sublevels due to extra repulsion of electrons paired in orbitals, making them easier to remove• Tends to decrease down a group

Ionization Energy Definition: the energy required to remove an electron from an atom

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