I. Waves & Particles(p. 91 - 94)

Ch. 4 - Electrons in Atoms

A. Waves

Wavelength () - length of one complete wave

Frequency () - # of waves that pass a point during a certain time period hertz (Hz) = 1/s

Amplitude (A) - distance from the origin to the trough or crest

A. Waves

Agreater

amplitude

(intensity)

greater frequency

(color)

crest

origin

trough

A

B. EM Spectrum

LOW

ENERGY

HIGH

ENERGY

B. EM Spectrum

LOW

ENERGY

HIGH

ENERGY

R O Y G. B I V

red orange yellow green blue indigo violet

B. EM Spectrum

Frequency & wavelength are inversely proportional

c = c: speed of light (3.00 108 m/s): wavelength (m, nm, etc.): frequency (Hz)

B. EM Spectrum

GIVEN:

= ?

= 434 nm = 4.34 10-7 m

c = 3.00 108 m/s

WORK: = c

= 3.00 108 m/s 4.34 10-7 m

= 6.91 1014 Hz

EX: Find the frequency of a photon with a wavelength of 434 nm.

C. Quantum Theory

Planck (1900)

Observed - emission of light from hot objects

Concluded - energy is emitted in small, specific amounts (quanta)

Quantum - minimum amount of energy change

C. Quantum Theory

Planck (1900)

vs.

Classical Theory Quantum Theory

C. Quantum Theory

Einstein (1905)

Observed - photoelectric effect

C. Quantum Theory

Einstein (1905)

Concluded - light has properties of both waves and particles

“wave-particle duality”

Photon - particle of light that carries a quantum of energy

C. Quantum Theory

E: energy (J, joules)h: Planck’s constant (6.6262 10-34 J·s): frequency (Hz)

E = h

The energy of a photon is proportional to its frequency.

C. Quantum Theory

GIVEN:

E = ? = 4.57 1014 Hzh = 6.6262 10-34 J·s

WORK:

E = h

E = (6.6262 10-34 J·s)(4.57 1014 Hz)

E = 3.03 10-19 J

EX: Find the energy of a red photon with a frequency of 4.57 1014 Hz.

II. Bohr Model of the Atom(p. 94 - 97)

Ch. 4 - Electrons in Atoms

A. Line-Emission Spectrum

ground state

excited state

ENERGY IN PHOTON OUT

B. Bohr Model

e- exist only in orbits with specific amounts of energy called energy levels

Therefore…

e- can only gain or lose certain amounts of energy

only certain photons are produced

B. Bohr Model

1

23

456 Energy of photon depends on the difference in energy levels

Bohr’s calculated energies matched the IR, visible, and UV lines for the H atom

C. Other Elements

Each element has a unique bright-line emission spectrum.

“Atomic Fingerprint”

Helium

Bohr’s calculations only worked for hydrogen!

C. Other Elements

Examples: Iron

Now, we can calculate for all elements and their electrons – next section

III. Quantum Model

of the Atom(p. 98 - 104)

Ch. 4 - Electrons in Atoms

A. Electrons as Waves

Louis de Broglie (1924)

Applied wave-particle theory to e-

e- exhibit wave properties

EVIDENCE: DIFFRACTION PATTERNS

ELECTRONSVISIBLE LIGHT

B. Quantum Mechanics

Heisenberg Uncertainty Principle

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 # of solutions quantized energy levels

defines probability of finding an e-

B. Quantum Mechanics

Radial Distribution CurveOrbital

Orbital (“electron cloud”)

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

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 )

Main energy level occupied the e-

Size of the orbital

n2 = # of orbitals in the energy level

C. Quantum Numbers

s p d f

2. Angular Momentum Quantum # ( l )

Energy sublevel

Shape of the orbital

C. Quantum Numbers

n = # of sublevels per level

n2 = # of orbitals per level

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

C. Quantum Numbers

3. Magnetic Quantum Number ( ml )

Orientation of orbital around the nucleus

Specifies the exact orbitalwithin each sublevel

C. Quantum Numbers

px py pz

C. Quantum Numbers

Orbitals combine to form a spherical shape.

2s

2pz2py

2px

C. Quantum Numbers

4. Spin Quantum Number ( ms )

Electron spin +½ or -½

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

C. Quantum Numbers

1. Principal # 2. Ang. Mom. # 3. Magnetic # 4. Spin #

energy level

sublevel (s,p,d,f)

orientation

electron

Pauli Exclusion Principle

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

Each e- has a unique “address”:

Feeling overwhelmed?

Read Section 4-2!