Lecture 2010/19/05. wavelength Amplitude Node Electromagnetic Radiation (Light as waves) Moving Waves.

Lecture 20 10/19/05

wavelength

wavelength

Amplitude

Node

Electromagnetic Radiation (Light as waves)

Moving Waves

c = λν

c = speed of light (3 x 108 m/s in a vacuum)

λ = wavelength (m)

ν = frequency (s-1 or Hertz, Hz)

Electromagnetic RadiationElectromagnetic Radiation

Red light has Red light has = 700 nm. Calculate the = 700 nm. Calculate the frequency.frequency.

Freq = 3.00 x 108 m/s

7.00 x 10-7 m 4.29 x 1014 sec-1Freq =

3.00 x 108 m/s

7.00 x 10-7 m 4.29 x 1014 sec-1

700 nm • 1 x 10 -9 m

1 nm = 7.00 x 10 -7 m700 nm •

1 x 10 -9 m

1 nm = 7.00 x 10 -7 m

Standing (stationary)

Waves

•Has 2 or more nodes

•Distance between nodes is λ/2.

•Distance between ends has to be n(λ/2)

a) Draw a standing wave with 1 node. What is the wavelength of this wave?

b) Draw a standing wave with 3 nodes between the ends. What is the wavelength?

c) If the wavelength of the standing wave is 2.5 cm, how many waves fit within the boundaries? How many nodes?

Visible Light

1. Which color in the visible spectrum has the highest frequency?

2. Is the wavelength of x-rays longer or shorter than UV?

The frequency of radiation used in microwave ovens is 2.45 GHz (1 gigahertz is 109 s-1.

What is the wavelength in nm of this radiation?

Light as particles

•Max Planck-

•Vibrations are quantized

•Planck’s constant

•E=hν = hc/λ

•E = energy (J)

•h = Planck’s constant

•6.626 x 10-34 J-s

Photoelectric Effect

Photoelectric EffectPhotoelectric Effect

Classical theory said that Energy of ejected electron should increase with increase in light intensity

NOT OBSERVED

No e- observed until light of a certain minimum E is usedNumber of e- ejected depends on light intensity.

Light consists of particles called PHOTONS of discrete energy.

Photoelectric Effect

Eelectron = Elight - Eejection

Compare the energy of a mole of red light photons (λ= 700 nm) and a mole of UV photons (λ= 300 nm)

KJ/mol 1.399J/mole 399126E

e)photon/mol 1002.6(photon/J1062.6E

nm10

m 1)nm 300(

)sm1000.3)(sJ1063.6(E

2319

9

834

λ

hchνE

KJ/mol 171J/mole054171E

e)photon/mol 1002.6(photon/J1084.2E

nm10

m 1)nm 700(

)sm1000.3)(sJ1063.6(E

2319

9

834

λ

hchνE

Dual Nature of Light

Both wave and particle characteristics

WaveRefractionDiffraction

ParticlePhotoelectric effect

DiffractionLight bends as it moves through a slit or around

a boundary

Refraction

Bending of light as it passes between materials of different optical density.

Line Emission Spectrum

“Excited” atoms emit light

Line Emission Spectrum

Balmer series

17

22

m100974.1)ttancons Rydberg( R

2n whereinteger, an is n

n

1

2

1R

λ

1

Rydberg equation

Balmer Series

Atomic Spectra and Atomic Spectra and BohrBohr

Atomic Spectra and Atomic Spectra and BohrBohr

1.1. Any orbit should be possible and so is any energy.Any orbit should be possible and so is any energy.

2.2. But a charged particle moving in an electric field But a charged particle moving in an electric field should emit energy. should emit energy.

Electron would eventually run out of energyElectron would eventually run out of energy

+Electronorbit

BohrBohr

New theory : New theory : Quantum or Wave Mechanicse- can only exist in certain discrete orbits e- can only exist in certain discrete orbits

Stationary statesStationary states e- is restricted to e- is restricted to QUANTIZEDQUANTIZED energy states. energy states.

levelenergy n

light of speed c

constant sPlanck'h

m100974.1constant RydbergR

n

RhcE

n

1

n

1hcR

n

1

n

1Rhc

λ

1hc

λ

hcE

n

1

n

1R

λ

1

7

2n

22

21

22

21

22

21

n= principal quantum numbern is an integern with the lowest possible energy is said to

be in the ground state

Electrons with higher energy than ground state are said to be in an excited state

Calculate the energies of n=1, n=2, and n=3 states of the hydrogen atom in J/atom.

R = 1.097 x 107 m-1

h = 6.626 x 10-34 J-s

c = 2.998 x 108 m/s

s/m10998.2light of speed c

sJ1062.6constant sPlanck'h

m100974.1constant RydbergR

2n and 1n

n

1

n

1Rhc

n

Rhc

n

RhcEEE

8

34

7

2initial

2final

2initial

2final

initialfinal

Moving between energy levels

Calculate the wavelength of the green light of excited H atoms.