ch2 sec 3and4

8/3/2019 CH2 Sec 3and4

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THE PHOTOELECTRIC EFFECT

The phenomena of the emission of electrons from a metallic surface when

exposed to EM radiation.

Electrons ejected from the surface in this way are called Photoelectrons .

The experimental setup that exhibits the photoelectric effect is as follows:

An evacuated tube contains two electrodes connected to a source of

variable voltage.

Surface of the metal plate is irradiated as the cathode.

Electrons reaching anode constitude a current called photoelectric

current measured by ammeter A.

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Experimental results

I) Curve shows how the current i varies as V and light intensity I:

Observe that:

1) The photoelectric current i depens on the anode potential:

2) V<0:

Thus, the minimum potential VStop. at which the photoelectric current dropst

to zero must equal to kinetic energy of the fastest electrons ejected:

.

2

max

2

1

StopeV mvK : Energy of the fastest electrons

3) The stopping potential is the same for intense and weak light.

4) The Photoelectric current i is proportional to the intensity of light I.

5) The Photoelectric current i appears without delay when the light is

applied.

A negative anode repels the

electrons. Only the fastest make it to

anode . The i steadily decreases as V

becomes increasingly negative until

at the VStop., All the electrons

are turned back and i terminates.

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II)

Observe that:

1) KE is proportional to the frequency , but NOT intensity I.

2) Photoelectrons are emitted only if light shining on metal will

have a frequency with0, where 0 is a treshold (or cut-

off) frequency. The value of 0 depends on the type of metal

from which the cathode is made . F.Ex.

0=5.6 x 1014 Hz for sodium

0=7.8 x 1014 Hz for calcium

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LIMITS OF CLASSICAL INTERPRETATION

According to classical EM theory;

I) because the energy in an EM wave is supposed to be spread

across the wavefronts, fairly straightforward calculations

show that a peroid of time should elapse before an individual

electron accumulates enough energy to leave the surface.

Experimental evidence is in sharp disagreement withthis.

II) Incident EM radiation (light) is considered as wave of

oscillation frequency and electric field amplitude E. In

this picture, electrons are ejected from the surface as a result

of an interaction between the oscillating electric field E of

the EM waves and the electric charge of electrons. Thus;

Kinetic Energy |Amplitude of oscillation|2

=|Amplitude of electric field|2=|E|2 ,

which gives the light intensity I.

Experimental evidence is in sharp disagreement with this,

too.

III) The existence of a cutt-off frequency can not be explained

by the classical EM theory of light, since according to this

theory photoelectric effect should occur at any of the

incident light provided that light is intensive enough.

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THE QUANTUM THEORY OF LIGHT

In 1905, A. Einstein resolved the paradox through the formulation

of the photon theory and he received the Nobel Prise in 1921 for

this work.

He generalised the Plancks notation that it was the absorption and

emission of radiation that occured in quanta.

Instead, Einstein proposed that radiation itself consisted of quanta

of energy.

Basic Postulates of the Einsteins Photon Theory:

EM radiation consists of zero rest mass particles called

photons that travel at the speed of light c, with energy

h .

Energy content of EM radiation of frequency in a radiant

source can only be an integral multiple of the quantity h:

nh E .

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The photoelectric effect by the Photon Theory

Increasing the intensity of light will increase the number of photons. Then

number of photoelectrons will increase too, so that photoelectric current i

increases, as observed.

However, instead, if the frequency is increased, the energy of each photon

h will then increase so that the photoelectrons will have more energy.

The Photoelectric Effect Experiment provides an important

confirmation of the particle nature of radiation.

According to Photon theory ,

light is composed of localised

bundles of EM energy called

photons and at frequency , the

nergy of a photon is h .

When striking the metal surface,

a photon interacts with a single

electron and ejects it from the

surface.

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The Explanation of the existence of a critical frequency0

in

The Photon Theory:

According to the Einsteins formulation, the fhotoelectric effect in a

given material should obey the equation:

hK max

with

0h : The work function , which is the minimum energy for

an electron to escape from a surface ( or else electrons

would pour out all the time)

Through the photon concept, the interaction between surface

electrons and incident EM radiation is a particle-particle

interaction.

If the photon energy is greater that the work function of the

metal, h , then electrons absorb the photon and partiallyuse the photon energy to overcome the work function. Then

rest of the energy appears as the kinetic energy for the electron.

On the other hand, if h , the surface electrons can not

accept this amounts of energy since interaction is particle-

particle like. Hence, no photon can liberate an electron if its

energy is less that the work function of the metal, irrespective

of the number of photons falling on it. Thus, when0,

which implies that Kmax<0 !, electrons will never be ejected

from the surface: Photoelectric effect is not observed below a

certain cut-off frequency0 .

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WHAT IS LIGHT?Today all physicists accept that the photoelectric effect (and many

other experiments) demonstrate beyond doubt the particle nature of

light. But, there are also many experiments that had established the

wave nature of light.Were these experiments somehow wrong? The

answer is that both kinds of experiments are right: Light exhibits wave

properties and particle properties. We can think of light as having a

dual character: The wave theory of light and the quantum theory of

light complement each other. Either theory by itself is only the part of the story and can explain only certain effects. The true nature of light

includes both wave and particle nature, even though there is nothing in

everyday life to help us visualize that.

ch2 sec 3and4

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