Structure and Properties of Matter 3.3 The Quantum Mechanical Model of the Atom 3.4 Quantum Numbers

Louis De Broglie

Light has properties of particles, and particles have properties of waves...applied this concept to the electron in a hydrogen atom (matter exhibits wave-particle duality). • DeBroglie assumed that any particle (including electrons) could also travel in waves

Erwin Shrödinger

Used matter waves to explain line spectra of multi-electron atoms.

Developed the Schrödinger wave equation (a wave function).

Equation includes four quantum numbers: n, l, ml, and ms.

Different combinations of these quantum numbers yield different solutions.

Each solution gives a probability region (orbital) where an electron is likely found.

Schrödinger's equation matched Bohr's results for hydrogen and extended to multi-electron atoms.

Werner Heisenberg

Heisenberg's Uncertainty Principle • It is impossible to know the exact position and speed of an electron at a given time. • The best we can do is to describe the probability of finding an electron in a specific location (electron probability distribution= derived from wave equations)

Quantum Mechanics (4)

Uses mathematical equations to describe the wave properties of subatomic particles

The region around the nucleus where an electron has a high probability of being found is called an orbital

. • These orbitals overlap, rather than being distinct levels as in the Bohr model.

• Electrons can be in different orbitals (or clouds) by absorbing or emitting quanta of energy •

The location of electrons is given by a probability distribution.

orbital

• The region around the nucleus where an electron has a high probability of being found

orbitals overlap

, rather than being distinct levels as in the Bohr model. • Electrons can be in different orbitals (or clouds) by absorbing or emitting quanta of energy

orbits vs orbital

Orbits

- Bohr - 2-dimensional ring - Electron is a fixed distance from nucleus - max. # of electrons per orbit depending on level

Orbital

Quantum Mechanics - 3-dimensional space - Electrons are a variable distance from nucleus - 2 electrons per orbital

Principal Quantum Number → n (describes, allowed vals?)

• describes the size and energy of an orbital • allowed values: n = 1,2,3,...to ∞ ("shells") •

formula for greatest number of electrons

greatest number of electrons possible in each energy level is 2n2

Secondary Quantum Number → l (describes, allowed vals?)

describes the shape of the orbital (= subshell number) • allowed values: l = 0 to (n -1) • each subshell number corresponds to a letter: • each subshell has a different shape with the highest probability of finding an electron

Magnetic Quantum Number → ml

describes the orientation of the orbital relative to other orbitals in the atom. • allowed values: ml= -l to+l • 3 dimensions (xyz-axis)

Spin Quantum Number → m

• describes the spin of the electron • electrons can have one of two possible spin values: - spin-up/clockwise (+½) - spin-down/counter clockwise (-½). *Any two electrons occupying the same orbital must have opposite spins

Pauli Exclusion Principle

No two electrons in an atom can have the same set of 4 quantum numbers (n, l, ml and ms ).