Chapter 45 The Nature of Light

LightParticle (photon)

Wave (electromagnetic wave)

Interference Diffraction Polarization

Light

Particle (photon)

Wave (electromagnetic

wave)

Interference Diffraction

Polarization

Black-body radiation

Photoelectric Effect

Compton Effect

hE energy

momentum

h Planck constant

h=6.63×10-34 J·sh

p Light is neither a classical particle nor a classical wave.

mass 2c

hm

Light is both a particle and a wave.

Cavity radiation:

The radiation emerging from the hole should not depend on the material or the mode of construction of cavity but only on the temperature.

Black-body radiation

Thermal Radiation)(R

max

total power per area

4-2-8

4

KmW1067.5

)(

TTI

radiation emitted by a body because of its temperature.

Stefan-Boltzmann law

d),( TR

0

d),()( TRTI

A metal plane with size of 0.01m2, what is power of the radiation at 400K?

W

I

5.14

40001.01067.5 48

W

I

232

80001.01067.5 48

Wien displacement law

m bT

)(R

increasing T

max

With a m of 500 nm for sun radiation, what is the temperature of sun:

1063 6 m Tb -

m

Km10898.2 3 b

4-2-8

4

KmW1067.5

)(

TTI

max

A metal plane with temperature of 800K, what is the maximum wave length of the radiation?

6000 KbTm

sun

R(λ,T)

Rayleigh-Jeans’ formula

Wien’s formula

Find the function R(λ,T) with λ. Wien’s formula

T

C

eC

TR

2

51),(

Rayleigh-Jeans’ formula

ckTTR 4

2),(

Planck’s radiation law (1900)

1

12),(

/5

2

kThce

hcTR

Planck’s radiation law

Max Planck assumed energy of harmonic oscillator is quantized. E

= hvh=6.626 ×10-34 Joule sec

Light is also a particle

1. Intensity problem If light of a given wavelength falls on a given emitter, the stopping potential does not depend on the intensity of the incident light. (stopping potential)

tSAxAc

SVuU dddd 0V VΔ

0

stopping potential

Negative pole

positivepoleThe Photoelectric Effect

Problems facing to classical physics

IA

P

tA

US

d

dEB0

1

Negative pole

positivepoleThe Photoelectric Effect

Problems facing to classical physics

2. Frequency problem

The frequency of the light must be greater than a certain value f0. Otherwise the photoelectric effect will not occur. (cutoff frequency)

3. Time delay problem

Photoelectrons are emitted without

delay once the incident light reaches

the surface of the emitter. (<10-9 s)0V VΔ0

stopping potential

tSAxAc

SVuU dddd

IA

P

tA

US

d

dEB0

1

S is dependent on E and B but not on the frequency of the light

Einstein’s analysis of the photoelectric effect

Light quantum (later comes photon) was first introduced by Einstain

Intensity of light, the number of photon, but the energy of a photon is the same.

function work is 2

1 2

mvKh

0V VΔ0

stopping potential

Negative pole

positivepole

1. Intensity problem2. Frequency problem3. Time delay problem

A single photon carries an energy hinto the emitter, where it is transferred to a single electron. There is no time delay.

Einstein’s analysis of the photoelectric effect

Light quantum (later comes photon) was first introduced by Einstain

function work is 2

1 2

mvKh

0V VΔ0

stopping potential

Negative pole

positivepole

ee

hV

0

hK0eV

Stopping potential

Einstein’s analysis of the photoelectric effect

Light quantum (later comes photon) was first introduced by Einstain

function work is 2

1 2

mvKh

0V VΔ0

stopping potential

Negative pole

positivepole

Cut off frequency oh

chc

0

0

Max Planck assumed energy of a photon is

quantized. E = hv

h=6.626 ×10-34 Joule sec

The beginning of the full development of quantum physics.

More proof

The Compton Effect

intensity

The scattered x ray have intensity peaks at two wavelengths, λ and λ´, λ´-λ= >0. varies with the angle φ.

Photon is already particle:

h

c

hphE ,

hh

K

Scattering by electron:

Kmchmch 22

,cos)/(1

cos2

cv

mvhh

2

22

)/(1 cv

mchcmc

hc

sin)/(1

sin2cv

mvh

]1)/(1

2

)/(1

1[)(

'2)(

22222

22

cvcvcm

hhh

]1)/(1

1[

2

2

cv

mchchc

2

22

22

)/(1

)()(cos2)(

cv

mvhhh

,cos)/(1

cos2

cv

mvhh

]1)/(1

1[)cos-(1

2

222

cv

cmh

)'

(hchc

m ')cos-(1mc

h

The Compton Effect

intensity

)cos1(' mc

h

does not depend on the wavelength of the incident radiation.

nm00243.0mc

hC

)cos1( c

Photon is already particle:

h

c

hphE ,

hh

K

0.0007nm

0.01nm 045

' ? ?K

' (1 cos )h

mc ' 0.0107nm

Scattering by atom?

'

hc hcK

151.29 10 J 38.06 10 eV

cos x

h hp

sin y

hp

y

x

ptg

p 027

?

LightParticle (photon)

Wave (electromagnetic

wave)

InterferenceDiffraction

Polarization

Compton Effectphotoelectric effect

Black-body radiation

New work

h

c

hphE ,

2

hm

c

In 1986, P. Grangier et al made chief modification for source S:

The experiment worked brilliantly.

Slowing Down Atoms by Photon Bombardment

The atoms can be slowed down from these high speeds by being bomdarded with photons. This will provide further direct and convincing experimental evidence of the validity of the photon concept.

vmhmvhmv fi Δ ,

At room temperature vrms=(3kT/m)1/2=430m/s

iv

h

Tv KT 7108.1 Laser cooling210 /rmsv m s

Steven Chu et al shared the 1997 Nobel Prize in Physics “for development of method to cool and trap atoms with laser light”.

Exercises

P1031-1032 11, 19, 21, 25, 31