Dualisme Cahaya Sebagai Gelombang dan Partikel

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Dualisme Cahaya Sebagai

Gelombang dan Partikel

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Wave Properties

Light intensity = ?????? ∝ ??????

Particle Properties

Light intensity: ?????? = ??????ℎ??????

Quantum Theory of Light

Under a constant frequency, the smallest

energy unit of light is quantized.

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For one photon

For N photon

I= ??????ℎ??????

?????? = ℎ?????? =

ℎ??????

??????

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Spectrum of electromagnetic radiation

Free electrons in resonance

Transition of bound electrons in atoms

Nucleus

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1.3.2 Photoelectric effect

http://lectureonline.cl.msu.edu/~mmp/kap28/PhotoEffect/photo.htm

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Photoelectric effect applet

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Einstein’s interpretation



h

E



Under a constant frequency, the smallest

energy unit of light is quantized.

One photon can at most

release one electron,

regardless of the photon

energy

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Work Function, W– the minimum energy for

electron to escape from the metal surface

W

K

hf





where K is the kinetic energy of the photoelectron

Photocurrent

nq

I

p





where



is the quantum efficiency, n number of

photons striking to the electrode per second, q

electron charge

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The number of photons striking to the electrode is

related to the light intensity I

L



h

A

I

n

L



Where A is the area of the electrode exposed to

light.

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Threshold frequency

When K = 0, there is no photoelectrons. The

frequency reaches the threshold frequency, i.e.

W

h

o





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Stopping voltage

The reverse biasing voltage: where the photoelectrode

is positively biased and the other negatively biased.

When the biasing

voltage increases

from zero, the

photocurrent

decreases. At V



= 0

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Stopping voltage

S

qV

K





v

The physical meaning is that the potential

difference barrier is decelerating the electron,

and finally consumes all its kinetic energy. Thus,

the stopping voltage gives us a tool to determine

the kinetic energy,

mgh

1

mv

K

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Stopping voltage against frequency

W

h

K

qV

S







q

W

q

h

V

S







Stopping

Voltage

V

S



Slope = /

h q



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Observations

• Monochromatic light is incident to one of the

electrodes made by a particular metal. The

induced current called photocurrent is

collected.

• If V is fixed, there exists a threshold frequency



o

, below which there is no photocurrent.

• Different electrode materials have threshold

frequency



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Observations

• The photocurrent is constant above the threshold

frequency under a constant illumination, regardless of

the frequency.

• The photocurrent is proportional with the intensity.

• The energy of electron is proportional with the

frequency.

• For a particular electrode and frequency of light, a

stopping voltage V

s

exists. No photocurrent can be

collected regardless of the intensity of light.

• There is no measurable tie lag between the illumination

of light and the release of photoelectrons. (10

-9

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Graphical presentations

Energy of photoelectrons is

proportional to the frequency;

Existence of threshold frequency



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Photocurrent is proportional to light

intensity

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Different frequency of light has different

stopping voltage

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Stopping voltage varies with

(1)electrode material for the same

frequency

(2) increases with frequency of light for

the same electrode

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Example:

Cahaya ultraviolet dengan panjang gelombang 350 nm dan intensitas 1 W/m

mengenai permukaan elektroda yang “work function” nya 2.2 eV.

a. Hitung energi kinetik elektron yang dilepas oleh elektroda tersebut.

b. Jika 1% dari photon yang datang diubah menjadi fotoelektron, berapa jumlah

elektron yang dilepas per detik jika luas permukaan 1 cm

Diketahui konstanta Planck =6.626x10

−34

Js = 4.136x10

−15

eVs

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Failure of classical theory

• In 1902, Philipp Eduard Anton von Lenard

observed that the energy of the emitted

electrons increased with the frequency of the

light. This was at odds with James Clerk

Maxwell's wave theory of light, which

predicted that the energy would be

proportional to the intensity of the radiation.

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• Within the experimental accuracy, (about 10

-9

second), there is no time delay for the emission

of photoelectrons. In terms of wave theory, the

energy is uniformly distributed across its

wavefront. A period of time is required to

accumulate enough energy for the release of

electrons.

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1.3.1 What is blackbody?

• Under thermal equilibrium, an object of a finite

temperature emit radiation (supposed to be EM

wave).

• It is found that an object that absorbs more also

emits more radiation.

• A perfect absorber is an object with black surface

that must of the incident energy is absorbed. It is

also expected to be a perfect radiator.

• Consequently, a blackbody is a perfect radiation.

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Phenomena for a blackbody

• Temperature-dependence emission spectrum.

• Reciprocal relation between wavelength at the peak

intensity



max

and ambient temperature T

• Inconsistency between observed spectrum and the

prediction from classical theory (Reyleigh and Jeans)

• A model suggested by Planck (quanta of light energy)

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Inconsistency of Classical wave theory and

experiment





kT

I

)

exp(





kT

hc

hc





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Temperature dependence of emission

spectrum

http://surendranath.tripod.com/AppletsJ2.html

http://webphysics.davidson.edu/alumni/MiLee/java/bb_mjl.htm

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Classic: Rayleigh – Jeans Formula

Planck Radiation

?????? = ??????

??????

Total Energy in the cavity with frequency interval between v and v+dv

?????? ?????? ???????????? = ?????? ?????? ?????? ???????????? =

8????????????

??????

????????????

?????? =

ℎ??????

exp

ℎ??????

??????

?????? − 1

?????? ?????? ???????????? = ?????? ?????? ?????? ???????????? =

8??????ℎ

??????

exp

ℎ??????

??????

?????? − 1

????????????

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Inconsistency of Classical wave theory and

experiment





kT

I

)

exp(





kT

hc

hc





Blackbody radiation – Stefan’s Law

An object having a surface temperature T will emit radiation power P which is

proportional to the surface area A of the object and to the fourth power of the

temperature.

4

AT

P







is the Setfan’s constant and is equal to 5.67 x 10

-8

-2

-4

(Jm

-2

-1

-4

)



is the emissivity of the object and is







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Stefan ‘s law

The total power (area

below a constant

temperature curve P)

4

AT





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Wein displacement Law

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-Hitung panjang gelombang yang dipancarkan tubuh anda

- Berapa energi yang dipancarkan oleh tubuh anda?

Blackbody radiation and ultra-violet catastrophe

as we do the integration

Blackbody radiation and ultra-violet catastrophe

From Maxwell E.M. theory we know that a dipole oscillating with frequency



will on average emits energy

(



)









(



) = const.



where

is the average energy of the oscillating dipole.

Rayleigh - Jean's Law

Maxwell-Boltzman distribution gives the energy state number density N(E) at energy E as

kT

E

e

E

N

)

(







total number of possible energy state







)

(

dE

E

N

and

Total energy







)

(

dE

E

EN

Hence the average energy:

states

energy

of

number

Total

nergy

Totale

E







kT

e

dE

Ee

dE

E

N

dE

E

EN

kT

E

kT

E





 







)

(

)

(

r()

Rayleigh-Jeans

Blackbody

radiation

catastrophe



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This result is in fact well known from kinetic theory where the energy of

vibrational degree of freedom

So now we have

r() 

Const.



Rayleigh-Jeans Law describes the beginning part of the blackbody radiation correctly at

low frequency (long wavelength) but it obviously wrong at high



. As



increases

r()

increases without limit, i.e. At , as we do the integration ,

r()

, the

radiate energy goes to infinity!

The energy of rotational / bending degree of freedom



kT













This is called UV catastrophe.

Ultra-violet catastrophe

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kT

e

dE

Ee

dE

E

N

dE

E

EN

E

kT

E

kT

E









 







)

(

)

(























n

kT

nE

n

kT

nE

e

e

nE

E

.....









kT

E

kT

E

kT

E

kT

E

kT

E

kT

E

e

e

e

e

E

e

E

e

E

(

)





x

(

)





x























.....

x

x

x

x

x

E

E

kT

E

e

x





)

(

x

x

E





)

(





x

E











kT

E

e

E

E

Planck's derivation of blackbody radiation

Rayleigh - Jean's Law:

This integration assume continuous distribution of energy, i.e. the oscillator can take up any value.

Plank made the hypothesis that the oscillator will only take up discrete energies

0, E

, 2E

, 3E

, .....etc.

the average energy is obtained from a summation instead of integration.

Let

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Blackbody radiation

http://surendranath.tripod.com/Applets.html

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Conclusion

• Rayleigh – Jeans ‘s derivation is only valid at

long wavelengths (low frequencies) and fails

at short wavelength.

• Planck made an assumption: energy emitted

from the radiator at a frequency



, E = nh



where n and integer, h the Planck constant

(energy is discretized)

• Implication: classical theory predicts energy is

continuous

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