*** Electrons in atoms absorb and release energy in specific quanta or packets.

*** Electrons have wave properties as defined by de Broglie’s equation:

l = h/(mv)

*** Electrons can’t be defined with a large degree of precision in terms of both position and energy at the same time. Heisenberg Uncertainty Principle:

Dx Dp > h

if we try to define position with a high degree of accuracy, Dx ® 0 then Dp ® ¥.

*** Therefore, electrons are acting as “particle-waves” in three dimensional space.

*** Wave equations are used to define behavior of the electrons. The solution to these differential equations give quantum numbers that define areas the electrons can be found.

n = principle quantum number, defines energy level

l = angular momentum quantum number, defines orbital shape

m_l = magnetic quantum number, defines orbital orientations

m_s = spin quantum number, defines spin direction

Wave Functions:

1. Only certain wave functions are allowed.

2. Each wave function corresponds to an energy level.

3. Therefore, the energy of the electron is quantized.

4. The square of the wave function gives the probability for finding the an electron.

Quantum Mechanics:

This is the theory of quantized electrons defined by wave equations.

Solutions (mathematical) to the wave equation yield quantum numbers that define the energy level, orbital shape and orientation for an electron.

Principal quantum number: n, (1, 2, 3 ……)

Describes the energy level of an electron

Azimuthal quantum number, l (0, 1, 2, ….. n-1)

Describes the orbital or subshell shape that the electron can be found in.

Magnetic quantum number, m _l, (-l, …. 0 ….. + l)

Describe the orientation in space of the orbital.

Spin quantum number, m_s, +1/2 or -1/2

Describes the spin orientation “up” or “down”