Quantum Mechanical

Model of the Atom

Modern Atomic Theory:

ReviewHypothesized that electrons could

only be at certain energy “levels”

This model had some serious problems.

Restricted the movement of electrons in certain orbits of specific and increasing radii

A. Electrons as Waves

Louis de Broglie (1924)

Applied wave-particle theory to electrons

Electrons exhibit wave properties

QUANTIZED WAVELENGTHS

A. Electrons as Waves

QUANTIZED WAVELENGTHS

A. Electrons as Waves

EVIDENCE: DIFFRACTION PATTERNS

ELECTRONSVISIBLE LIGHT

B. Quantum Mechanics

Heisenberg Uncertainty Principle

It is impossible to know both the velocity and position of an electron at the same time

B. Quantum Mechanics

σ3/2 Zπ

11s 0

eΨ a

Schrödinger Wave Equation

(1926)

finite number of solutions quantized energy levels

defines probability of finding an electron

B. Quantum Mechanics

Radial Distribution CurveOrbital

Orbital (“electron cloud”)

Region in space where there is 90% probability of finding an electron

Wave/Quantum Mechanical Model of the Atom

C. Quantum Numbers

UPPER LEVEL

Four Quantum Numbers:

Specify the “address” of each electron in an atom

C. Quantum Numbers

1. Principal Quantum Number ( n )

Energy level

Positive nonzero integers like 1, 2, 3, …

Size of orbital

n2 = number of orbitals in the energy level

C. Quantum Numbers

s p d f

2. Angular Momentum Quantum # ( l ) Energy sublevel (s, p, d or f)

sharp, principal, diffuse, fundamental l = n – 1 Shape of the orbital

C. Quantum Numbers

n = number of sublevels per energy level

n2 = number of orbitals per energy level

Sublevel sets: 1 s, 3 p, 5 d, 7 f

C. Quantum Numbers

3. Magnetic Quantum Number ( ml ) Orientation of the atomic orbital in space Specifies the exact orbital within each

sublevel ml = 2l + 1

C. Quantum Numbers

px py pz

C. Quantum Numbers

Orbitals combine to form a spherical shape.

2s

2pz2py

2px

C. Quantum Numbers

4. Electron Spin Quantum Number ( ms )

Electron spin +½ or -½

An orbital can hold 2 electrons that spin in opposite directions.

C. Quantum Numbers

1. n 2. l 3. ml

4. ms

energy level

sublevel (s,p,d,f)

orbital

electron

Pauli Exclusion Principle

No two electrons in an atom can have the same 4 quantum numbers.

Each electron has a unique “address”:

Types of Atomic Orbitals

The most probable area to find these The most probable area to find these electrons takes on a shapeelectrons takes on a shape

So far, we have 4 shapes. They are So far, we have 4 shapes. They are named s, p, d, and f. named s, p, d, and f.

No more than 2 electrons assigned to No more than 2 electrons assigned to an orbital – one spins clockwise, one an orbital – one spins clockwise, one spins counterclockwisespins counterclockwise

Shapes of Atomic Shapes of Atomic OrbitalsOrbitals

s orbitals orbital p orbitalp orbital d orbitald orbital f orbitalf orbital

Relative sizes of s - orbital

p Orbitalsp Orbitalsp Orbitalsp Orbitals

p sublevelp sublevel has has

3 orbitals3 orbitalsThese are called x, y, and zThese are called x, y, and z

p sublevelp sublevel has has

3 orbitals3 orbitalsThese are called x, y, and zThese are called x, y, and z

planar node

Typical p orbital

planar node

Typical p orbital

There is a There is a PLANAR PLANAR NODENODE thru the thru the nucleus, which is nucleus, which is an area of zero an area of zero probability of probability of finding an electronfinding an electron

3p3pyy orbital orbital

p Orbitalsp Orbitalsp Orbitalsp Orbitals

The three p orbitals lie 90The three p orbitals lie 90oo apart in apart in spacespace

d Orbitalsd Orbitalsd Orbitalsd Orbitals

d sublevel has 5 d sublevel has 5 orbitalsorbitals typical d orbital

planar node

planar node

Shapes of the five 3d orbitals

f Orbitalsf Orbitalsf Orbitalsf Orbitals

f sublevel has f sublevel has 7 orbitals7 orbitals

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