Part II. Waves & Particles Ch. 5 - Electrons in Atoms

Part II. Waves & Particles

Ch. 5 - Electrons in Atoms

QuantizedQuantized Energy vs. Energy vs. ContinuousContinuous

EnergyEnergy QuantizedQuantized Energy comes in Energy comes in

discrete packagesdiscrete packages ExampleExample: second : second

hand on clock that hand on clock that “ticks”“ticks”

STAIRSSTAIRS

ContinuousContinuous Energy is flowingEnergy is flowing ExampleExample: second : second

hand on clock that hand on clock that moves continuouslymoves continuously

ESCALATORESCALATOR

Dual Nature of Light……. Particle or Wave

• Remember a quantum of energy is the amount of energy to move an electron from one energy level to another.

• Energy is quantized therefore light must be quantized.

• These smallest pieces, quanta, are called ……photons : particles of light

• BUT, Energy is also continuous. Therefore light which is continuous acts like a WAVE

ThereforeTherefore……….……….

LLiigghhtt transmits energy as a transmits energy as a particleparticle

AndAnd

LLiigghht t travels through space as travels through space as a a wavewave

Quantum Theory

Einstein (1905)

Concluded - light has properties of both waves and particles

“ wave - particle duality ”

Wave-Particle DualityWave-Particle DualityJJ Thomson won the Nobel prize for describing the electron as a particle.

His son, George Thomson won the Nobel prize for describing the wave-like nature of the electron. The

electron is a

particle!

The electron is an energy

wave!

Wave-Particle DualityWave-Particle DualityJJ Thomson won the Nobel prize for

describing the electron as a particle.His son, George Thomson won the

Nobel prize for describing the wave-like nature of the electron.

The electron is a particle!The electron is an energy wave!

Wave-Particle DualityWave-Particle DualityJJ Thomson won the Nobel prize for describing the electron as a particle.

His son, George Thomson won the Nobel prize for describing the wave-like nature of the electron.

The electron

is a particle!

The electron is an energy

wave!

LLIIGGHHTT

A. Waves

Wavelength () - length of one complete wave

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

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

Parts of a wave

Wavelength

AmplitudeOrigin

Crest

Trough

High point

Low point

baseline of wave

Wavelength – distance from crest to crest

symbol: λ = “lambda”Amplitude – height of wave from the

origin to the peak; brightness, intensity of light

• Frequency – how frequently a way oscillates up & down; the # of times a wave completes a cycle of up & down motion

– Symbol is ν = “nu”– SI unit is Hertz (Hz) or cycles/sec (1s or

s-1)

Summary of LightSummary of Light

c =

E = hTherefore: energy is directly proportional to the frequency.

High frequency = high energy

Low frequency = low energy

Therefore: wavelength and frequency are indirectly proportional.

Short wavelength = high frequency

Long wavelength = low frequency

E = h

Energy of a wave – E (measured in joules)

Planck’s Constant 6.626 x 10-34 j*s

Frequency

c =

Speed of Light – 3 x 108 m/s

Wavelength

Frequency

Electromagnetic RadiationElectromagnetic Radiation ““LightLight””

The study of light led to the The study of light led to the development of the quantum development of the quantum mechanical model.mechanical model.

Light is a type of electromagnetic Light is a type of electromagnetic radiation.radiation.

Electromagnetic radiation includes Electromagnetic radiation includes many kinds of waves many kinds of waves

All light waves move at All light waves move at 3.00 x 103.00 x 1088 m/s m/s (c =the Speed of Light)

Relationship between Frequency & Wavelength

As Wavelength INCREASES, frequency ________________

As Wavelength DECREASES, frequency _______________

DECREASES

INCREASES

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, 1/s or s-1)

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 s-1

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

C. Quantum Theory

E: energy (J, joules)h: Planck’s constant (6.6262 10-34 J·s): frequency (s-1)

E = h

The energy of a photon is proportional to its frequency.

C. Quantum Theory

GIVEN:

E = ? = 4.57 1014 s-1

h = 6.6262 10-34 J·s

WORK:

E = h

E = (6.6262 10-34 J·s)(4.57 1014 s-1)

E = 3.03 10-19 J

EX: Find the energy of a red photon with a frequency of 4.57 1014 s-1.

Quantum Theory

Planck (1900)

vs.

Classical Theory Quantum Theory