26.3 Wave Functions and Atomic Orbitals

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Wave Functions and Atomic Orbitals

Wave Functions

The Schroedinger equation relates the energy of an electron to a wave equation (ψ).

ψ² yields the probability of finding an electron in a particular volume of space.

HEISENBERG UNCERTAINTY PRINCIPLE
• It is impossible to simultaneously know an electron’s position (x) and momentum (mv) with infinite precision.

QUANTUM NUMBERS
	NAME	WHAT IT MEANS	WHAT IT MEANS
n	Principal	Shell #	[ 1 ... ∞ ]
l	Orbital (Azimuthal)	Subshell (type of orbital) 0=s; 1=p; 2=d; 3=f	[ 0 ... (n-1) ]
m_l	Magnetic	Orientation (specifies a single orbital)	[ -l ... +l ]
m_s	Spin	Spin up or spin down	+1/2 or -1/2
Pauli Exclusion Principle		No two electrons in an atom can have the same set of four quantum numbers.

• There are n² orbitals in each shell which can hold a maximum of 2n² electrons:

• The K shell has 1² or 1 orbital which can hold a maximum of 2 electrons.

• The L shell has 2² or 4 orbitals which can hold a maximum of 8 electrons.

• The M shell has 3² or 9 orbitals which can hold a maximum of 18 electrons.

• The N shell has 4² or 16 orbitals which can hold a maximum of 32 electrons.