Compton effect (English)

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3-7: The Compton Effect

As learned

on the preceding page,

Einstein proposed

the hypothesis of light quanta

and succeeded

in the explanation

of the photoelectric effect.

As a result,

it has been established

that light exists

in the space

as grains

(or corpuscles or particles)

with energy .

The particle nature

corpuscular nature

of light

was more firmly

established by

the discovery of

the Compton effect.

In 1923,

A. H. Compton

(USA, 1892 - 1962)

discovered that

the scattering of

X rays by a crystal

can be explained well

on the basis

of the particle nature

of light.

(Of course, the phenomenon

that X rays are scattered

by crystals had been

well-known before.)

The scattering of X rays

by a particle

(an electron at present)

is sometimes called

Compton scattering.

Compton found that,

if we consider

that X rays collide

with the electrons

in a crystal

as if they were balls

of billiard,

Compton scattering

could be explained well.

To formulate this process,

we have to define

the momentum of a light quantum.

[Momentum of a Light Quantum]

It has been discussed

that a light quantum

is a "particle" with

energy .

This "particle" is considered

to carry a momentum

at the same time,

because we know that

light gives

a pressure on the

surrounding wall.

How large is the amount

of the momentum?

Let us study this below.

Consider a container

filled with light

of frequency .

Let the pressure

given on the wall

of the container

by the light

be P and

the energy of the

light per unit volume

be U.

We have a relation

which is proved

by experiment.

(This relation

can also be derived

from the classical theory.)

From this relation,

we see that

the momentum p

of a light quantum

is given as

Namely,

we can say that

the momentum of a light quantum is given by dividing the energy by the light speed.

This result

can be obtained

by a method similar to

that through

which we derived

the relation between

the molecular motion

in a gas and its pressure.

Let us explain this

on the other page:

3-7-A: Momentum of Light Quantum

If you feel it tedious,

you may skip this.

[The Compton Effect by the Hypothesis of Light Quanta]

Compton found that,

when the monochromatic X rays

are illuminated

on a graphite

(a kind of carbon crystal),

the wavelength

of the scattered X rays

would be longer

as the scattering angle

becomes larger.

This cannot be explained

with the classical theory.

In the classical theory

consisting of

Newtonian mechanics

and Maxwellian electromagnetism,

the incident X rays

oscillate the charged

particle

(electron at present)

and the oscillating

charged particle

radiates around the same

frequency of electromagnetic

waves (X rays).

Accordingly,

the frequency of the

radiated (scattered)

X rays

must be the same as

that of the incident X rays.

Compton analyzed

Compton scattering as follows.

He thought that

the incident X rays collide

against the electron

in the graphite

as a "particle"

with the energy .

and the momentum .

Suppose that the energy

and the momentum

of the X rays

scattered in the

scattering angle

are

and ,

respectively.

The electron

(the mass = m )

recoils

with a momentum mv.

The energies and momenta

in Compton scattering

are shown in

the following figure (A),

and the relation

of the momentum conservation

is in the following

figure (B).

The momentum conservation

relation is written

Since ,

we have

Inserting this

into the above momentum

conservation relation,

we get

On the other hand,

the energy conservation

is written

Therefore, the difference

between the the wavelength

of the incident

and scattered X rays becomes

Accordingly, the wavelength

of the scattered

X rays becomes

longer as the scattering angle

increases.

Compton's results

at the scattering angles,

and

are shown in the following

figure.

Each graph represents

the intensity of X rays

(ordinate)

as a function

of wavelength

(abscissa).

As the scattering angle

increases in the

above figure,

the intensity of X rays

separates into two peaks;

the right one of

the longer wavelength

shifts to longer region.

This wavelength

is well fit to

the formula presented above.

The wavelength

of another peak

is just the same as

that of the incident

X-ray beam.

This is that scattered

by the whole atom whose

mass is quite large,

so that the wavelength seems

not to be varied.

Thus the particle nature of X rays was

completely confirmed.

Incidentally,

the recoil electron

could not be detected

in Compton's experiment,

but, a little bit later,

its picture was taken

with

Wilson's cloud chamber.

[Photon]

After Einstein proposed

the hypothesis of light quanta

in 1905,

people have been doubtful

of the idea

of the particle nature

of light for

about 20 years.

However, once they look

at the experimental results

of the Compton effect,

they cannot help

convincing themselves

about the theory

of light quanta.

Then, the particle of light

(light quantum)

has been called

photon,

which has been admitted

into the brotherhood

of "particles"

like electrons or protons.

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