Bohr's theory and de-Broglie wave (English)

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1-1: Bohr's Quantum Theory and De Broglie Waves

[Bohr's Quantum Theory]

We learned on

the page,

4-3: The Bohr Model of Atoms

in the preceding Seminar,

that

the atomic structure

of hydrogen

that had been difficult

to be understood

with classical theory

was beautifully explained

by Bohr's quantum theory.

This theory

is sometimes called

the old quantum theory.

Here let us summarize

the main points

of the theory.

In Bohr's quantum theory,

it is considered

that an atom

can be described by

the Rutherford model of the nuclear atom,

in which a heavy nucleus

is surrounded by

light electrons

that move obeying

the classical theory.

Since this atomic model

brought about

some difficulties

discussed on

the pages,

2-7: Summary of Part 2

and

4-1: The Difficulty of the Rutherford Model of the Nuclear Atom

in the preceding Seminar,

Bohr added the

following hypotheses;

i.e.,

postulations of stationary state,

frequency condition,

and

quantum condition.

A schematic sketch of

the Rutherford model

of the nuclear atom

is represented in

the following figure,

in which

the central black sphere

is the atomic nucleus,

and the small points

denote the electrons

surrounding the nucleus.

While the atomic radius

is about ,

the nuclear radius

seems to be less

than 1/10000 of it.

The Rutherford Model of the Nuclear Atom

A black big ball

at the center

is the nucleus and

small red points moving

around the nucleus

are electrons.

By Bohr's

Quantum theory,

the structure,

especially the energy,

the radius, the stability

and the spectra

of hydrogen atom,

were explained

very well.

[De Broglie Waves]

As mentioned previously,

it was clarified

by the discovery of

the photon

that light

which had so far

been considered

to be wave

(electromagnetic wave)

has also a particle nature.

Then de Broglie

(France, 1892 - 1987)

thought that

such things as

electrons which

had so far been considered

to be particles

might possess wave nature

as well (1932).

This is the idea

of the de Broglie waves

or de Broglie's matter waves.

We know that,

in the case of light,

the frequency ,

and the wavelength ,

are connected respectively to

the energy E

and the momentum p

of photon

by means of

Einstein's relations

De Broglie assumed that

these relations (1)

might be valid

also for the de Broglie waves.

The above Einstein's

relations are

therefore called

Einstein - de Broglie's relations as well.

[The Evidences of De Broglie Waves]

C. J. Davisson

(USA, 1881 - 1958)

and

L. H. Germer

(USA, 1896 - 1971)

observed the interference

phenomena resulting from

an electron beam

reflected from

a single crystal of nickel,

and they confirmed

that the interference

was a perfect fit to

Einstein-de Broglie's relations.

At the same time,

G. P. Thomson

(UK, 1892 - 1975)

also confirmed

the wave nature of electrons

using a metallic multi-crystal.

(See the photograph of a diffraction pattern of electron beams

on the page,

4-4: in the preceding Seminar).

Moreover,

O. Stern

(Germany, 1888 - 1969)

observed the interference patterns

produced by projecting

beams of helium atoms

and hydrogen molecules

onto crystals,

and confirmed that

the results exactly

fit the

Einstein-de Broglie's relations.

Thereby

de Broglie waves accompanying

not only electrons but

also

general particles

were confirmed

experimentally.

[Bohr's Quantum Condition and De Broglie Waves]

Let us consider

a hydrogen atom with

Bohr's quantum theory.

In that theory,

the quantum condition

to determine the

stationary states

of the atom

seems to claim

that the circumference

of the orbit of the electron

revolving about the nucleus

should be an integral multiple

of the wavelength

of the de Broglie wave

of the electron.

This has already been discussed

on the page,

4-4: The Wave Nature of Electrons

in the preceding Seminar.

This quantum condition

says that

the de Broglie wave

of the electron must be

a continuous

standing wave

around the nucleus.

(See the following

figure.)

Bohr's quantum condition for a hydrogen atom.

In this figure,

the de Broglie wave

does not connect smoothly,

because the circumference

is not an integral multiple

of the wave length.

Namely, this figure

does not show

a correct de Broglie wave

in a hydrogen atom.

The circumference

of a true hydrogen atom

must be

an integral multiple

of the de Broglie wavelength.

We can easily

understand and explain

this quantum condition

by considering

the smooth continuity

of the de Broglie waves.

Thus we can realize that

the de Broglie waves play an essential role

underlying Bohr's

quantum theory.

They looked forward to

construction of

a really new theory

from which Bohr's quantum

theory itself

can be derived inevitably.

Such a theory is

nothing other than

Schroedinger's wave mechanics

or quantum mechanics.

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