Photoelectric Effect (English)

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3-6: The Hypothesis of Light Quanta
and the Photoelectric Effect

[Einstein's Hypothesis of Light Quanta]

As learned

on the preceding page,

it was clarified that

the energy of the radiation

(light) in a cavity

is integral multiples

of the elementary

unit .

This can never

be explained with

the classical theory

which consist of

Newtonian mechanics

and Maxwellian

electromagnetism.

The reason is as follows.

A cavity

in a thermal equilibrium

is exchanging energies

with the surrounding

wall every moment.

In exchanging energies,

the amounts of energies

being given

and taken

are equal in average,

and they are balanced.

However, they are

always fluctuating

from moment to moment.

Strictly speaking,

the energies being

given and taken

are not necessarily equal,

but always fluctuating.

Accordingly,

the total energy

of the cavity radiation

is always fluctuating.

The energy of the cavity

radiation must

be a collection of

the elementary quanta .

The energy fluctuation

must therefore be

an integral multiple

of the unit .

Hence a finite amount

of energy

is coming in

or going out

of the cavity.

Such a finite amount

of instantaneous energy

transfer is not allowed

in the classical theory.

Therefore Planck's idea

of energy quanta can

never be explained

within the classical theory.

In 1905,

Einstein proposed

a hypothesis

that the light (radiation) exists in a form of grains (or corpuscles or particles) in a space.

This is the

Einstein's hypothesis of light quanta.

[The Miraculous Year]

The year 1905

was a miraculous year

(annus mirabilis)

in the history of sciences.

In 1905, A. Einstein

published

three great papers,

each of which

may be worth being awarded

a Nobel Prize independently.

The first was

on the discovery of light quanta,

which contains the theory

of the photoelectric effect

as discussed below.

The second was

on the theory of Brownian motion,

which shows the real

existence of atoms

and molecules.

The third contained

the special theory of relativity.

An office worker

of the Berne Patent Office

published three great works

just in one year,

the amazing year of 1905.

This was nothing

other than a "miracle".

[The Photoelectric Effect]

A metal surface

that is illuminated

by light

emits charged particles.

This phenomenon

was discovered by

H. R. Hertz

(Germany, 1857 - 94)

while he was doing

experiments concerning

the electromagnetic waves.

One of his students,

P. E. A. von Lenard

(Germany, 1862 - 1947)

measured the

charge-to-mass ratio

of these particles

and confirmed

that the particles

are electrons (1900).

Hence this phenomenon

is called

the photoelectric effect.

A schematic drawing

of the apparatus detecting

the photoelectric effect

is shown in

the following figure.

The apparatus detecting the photoelectric effect

Two plates (electrodes)

are put

in a vacuum glass tube.

When ultraviolet rays

are illuminated

on the one of the plates,

an electric current flows

if the illuminated plate

is electrically negative

as Case (A),

but no current

if it is positive

as Case (B).

[Einstein's Theory on the Photoelectric Effect]

On the basis

of the hypothesis

of light quanta,

Einstein proposed

the following theory

about the

photoelectric effect

(1905).

This was contained

in the same paper

as the idea

of light quanta

was proposed.

Einstein thought

that the light

of a frequency

is existing

in a form of grains

(corpuscles or particles)

of the energy of

and absorbed as whole units

by electrons in a metal.

These whole units

are light quanta.

If the energy

gained by an electron

is greater than the energy

W necessary

to carry the electron

from inside to outside

of the metal,

then the electron

would be emitted

as a photoelectron.

Here

is called

the work function,

which has already

been known

by Richardson's research

on the thermal electrons.

( Richardson:

See the following

figure (C).)

[Millikan's Experiment on the Photoelectric Effect]

The above-mentioned

Einstein's theory

on the photoelectric effect

was proved by

Millikan's experiment

carried out in 1916.

The schematic drawing

of the apparatus

for Millikan's experiment

is shown in the above

figure (D).

The experimental results

are summarized

as follows:

(1)

If all the electrons

emitted by the photoelectric effect

are collected on the anode

by setting the voltage

rather high,

the electric current

flowing through the ammeter

would be proportional

to the intensity

of the light

illuminated on the cathode.

(2)

There is a threshold

frequency of the light

illuminated

on the cathode

for photoelectric emission.

If the frequency

of the light is

less than this threshold

value,

no photoelectrons

are released

no matter how intense

the illumination is.

(3)

The maximum kinetic energy

of the photoelectron

is independent of

the intensity of the light

illuminated.

(4)

The maximum kinetic energy

of the emitted electrons

is a linear function

of the frequency,

which is exactly

the same as Einstein's

hypothesis,

i.e.,

Millikan obtained

the constant h from

this experiment as

which is well fit

to the value obtained

by Planck's analysis

about the cavity radiation.

[Difficulty of the Classical Theory]

It is impossible

to explain

the above-mentioned

results of Millikan's experiment

within the classical theory

consisting of

Newtonian mechanics

and Maxwellian electromagnetism.

We can easily imagine

the followings

within the classical theory:

When a light is illuminated

on the surface of a metal,

electrons in the metal

are violently shaked

and oscillated

by the electromagnetic

field of the light.

If the oscillation

is too hard

to keep the electrons

inside the metal,

they jump out of

the metal surface.

According to the

classical theory,

the energy given

to the electrons

in this case

must be proportional

to the square of

the strength of

the electromagnetic field.

Hence the maximum energy

of the photoelectron

must be dependent

on the intensity

of the light illuminated.

This completely contradicts

Millikan's experimental results

summarized above,

in which

(2),

(3) and

(4)

can never be explained

with the classical theory.

Moreover, we cannot

explain the time

to produce the photoelectric effect

within the classical theory.

The emission of

the photoelectrons appears

practically instantaneous.

This cannot be explained

with the classical theory.

Let us discuss this below.

The value of

the work function

of standard metals is

Here let us discuss

the photoelectric effect

for a metal with

The energy of light

passing through an area

in 1 s (second)

at a distance

of 1 m from

a point source

of light at a rate

of 1 W (watt)

When we illuminate

this light on the metal,

the energy of the

light hit on an atom

since the cross section

of an atom is nearly

Suppose that the atom

would absorb all

this energy and

it would be given

to one electron in the atom,

and thereby a photoelectric

effect would occur.

More energy

than the value

of the work function

must then be

accumulated on the electron

before the emission.

It takes about 100 s for this.

This means that

the photoelectron

comes out about

100 s after switching

on the light source.

However the

photoelectric effect

occurs instantaneously

in practice.

Thus the classical

theory cannot explain

the photoelectric effect.

We could understand all

without any contradiction,

if we think

that light is

instantaneously absorbed

as a whole unit

of the energy

by the electron

in the metal.

This is Einstein's hypothesis

of energy quanta.

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