Summary of Part_2 (English)

2-7: Summary of Part 2

Let us summarize

what we have

learned in Part 2.

(1)

Through the discoveries

of the radioactivity

and the decay

of radioactive elements,

it has been realized

that an atom

has an internal structure

and is not

eternally constant

but

changeable.

(2)

An atom has

a structure in which

a massive nucleus

at the center

is surrounded by

light electrons.

(3)

The size of the atomic

nucleus is

very small;

its radius

is less than

(4)

The atomic nucleus

has also an

internal structure

and is a changeable

object.

The proton

is one of the constituents

of the nucleus.

[The Difficulty in the Rutherford Model]

In the solar system,

the planets are

revolving around

the sun.

In the Rutherford model,

the electrons are

considered

to move around

the nucleus.

The attractive force

between the sun

and a planet is

the universal gravitation.

On the other hand,

the force through

which the nucleus

attracts electrons

is the Coulomb force.

One might naively

suppose that

this Coulomb attractive

force

and the centrifugal force

due to the orbital motion

of the electron

are just in balance

to keep the system stable.

However,

this idea has

a serious difficulty.

Now, let us explain

this difficulty

taking the case of

hydrogen atom

in which an electron

(of mass m

and charge e )

is moving around a proton.

Suppose that,

since the proton mass

is large compared

with that of electron,

the proton stays

at rest at the origin

of the coordinate frame.

(A)

The balance

between the centrifugal

force and

the Coulomb force

is written

The quantity

on the left-hand side

is the strength of

the centrifugal force

and the right-hand side

the Coulomb force.

Here

r is the

radius of the orbit

of the electron,

i.e. the radius

of the hydrogen atom,

and v is

the speed of the electron.

The above equation

is rewritten

Looking at this

equation only,

we can think

that the radius

of the hydrogen

is inversely proportional

to the square

of the speed

of the electron,

so that the hydrogen

atom can have

an arbitrary radius

depending

on the speed v.

However, the realistic

hydrogen is not so;

the radius of the

realistic hydrogen

atom looks

constant always.

(B)

According to

the theory

of electromagnetism,

any accelerating charged

particle radiates electromagnetic waves,

with losing the energy.

Thus the electron

in the Rutherford model

must lose the energy

to become out of balance

and spiral inward,

and finally collapse

on the proton.

This means

that the hydrogen atom in the Rutherford model must be unstable.

In contrast to this,

however, a realistic

hydrogen atom

is quite stable

and does not collapse.

Rutherford was well

aware of this difficulty,

but he

chose to ignore

it temporarily.

Without solving

this stability problem,

we cannot look at

the true feature

of the microscopic world.

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