Quantum Mechanical Model of the Atom

BC High ChemistryMr. Olejnik

Review of Atomic Models• Bohr’s Model– Electrons move in definate orbits or

energy levels around the nucleus

Wave model of atom• Modern model of atom– According to theory of

wave mechanics electrons don’t orbit nucleus predictably

– Impossible to determine location of electron, we interpret it with a “cloud”.

Light as Waves• Wavelength = distance between the

crests of two subsequent waves (wave = λ “lambda”)

• Frequency = how often a wave crosses a fixed point (v)

Think1. Which of the following has the

longest wavelength (λ)2. Which of the following has the

highest frequency (v)

Speed of Light• Speed of light ≈ 3.00 x 108 m/s = C

• C = λv– Λ & v are inversely proportional so if λ increases, v

decreases etc.

Quantum Mechanical Model• Mathematical Model of the atom based on

the Quantum Theory, • Quantum Theory basically says:–Matter has properties associated with waves.– Impossible to predict the exact position of e-– E- have both properties of particles & waves

Quantum Mechanical Model• Developed in the 1920’s• Werner Heisenberg (Uncertainty

Principle)• Louis de Broglie (electron has wave

properties)• Erwin Schrodinger (mathematical

equations using probability, quantum numbers)

Werner Heisenberg: Uncertainty Principle

• We can not know both the position and momentum of a particle at a given time.

Louis de Broglie, (France, 1892-1987)

Wave Properties of Matter (1923)•Since light waves have a particle behavior (as shown by Einstein in the Photoelectric Effect), then particles could have a wave behavior.•de Broglie wavelength h

mv

Particle vs. Wave• Is light particles or waves?– YES!

Erwin Schrodinger, 1925

• Quantum (wave) Mechanical Model of the Atom– Complicated equation used to

estimate an e-’s location– 4 quantum numbers describe

the location of e- in an atom

Yikes! You DON’T need to know this!

Quantum Model of Atom• Quantum model of atom:– Pattern of e- arrangement in an atom, described by quantum

numbers.

• Quantum Numbers:– 4 numbers that describe the properties and position of an e-.

• Orbital:– A region in space in which there is high probability of finding an

electron.

Four Quantum Numbers• Principal Quantum Number = “n”– Main energy level of an e-

• Angular Momentum Number = “l”– Indicates shape

• Magnetic Quantum Number = “m”– Indicates oreintation

• Spin Quantum Number = “spin”– Indicates direction e- is spinning

Principal Quantum Number: “n”

• Indicates main energy levels– n = 1, 2, 3, 4…

Angular Momentum Number, “ℓ”

• Indicates shape of orbital sublevels

• ℓ = n-1

ℓ sublevel0 s1 p2 d3 f4 g Elements in specific regions of the

periodic table have similar shapes.

Orbital Shapes

Magnetic Quantum Number, ml

• Indicates the orientation of the orbital in space.– Basically which spot it occupies.

– Values of ml : integers -l to l

• The number of values represents the number of orbitals possible.

• Example: if n = 3, l= 2, ml = -2, -1, 0, +1, +2

so ml could be in any of these spaces:

___ ___ ___ ___ ___ -2, -1, 0, +1, +2

Which sublevel does this represent?Answer: d

Magnetic Quantum Number, ml

Electron Spin Quantum Number, (ms or s)

• Indicates the spin of the electron (clockwise or counterclockwise).

• Values of ms: +1/2, -1/2

Example 1:• Fill out this chart for the following

quantum numbers: (3, 2, -1, -1/2)

Example 2:

• List the values of the four quantum numbers for orbitals in the 3d sublevel.

• Answer: – n=3

– l = 2

– ml = -2,-1, 0, +1, +2

– ms = +1/2, -1/2 for each pair of electrons