A system of physical chemistry - Index of

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A SYSTEM OF PHYSICAL CHEMISTRY

and W = total energy necessary to remove all the charged particles to

infinite distances from one another = ~.—— , . . (lo)

For the **system** in question we have—

where 5,, has its former significance. It will be observed that Yq is a

function **of** the radius **of** the ring.

As regards the stability **of** the ring **of** electrons with respect to displacements

perpendicular to the plane **of** the ring, Bohr shows that the

**system** will not be stable unless when N = i, « = 2 or 3. Throughout

the entire treatment **of** the problem it will be observed that Bohr regards

the question **of** stability with respect to such "perpendicular" displacements

as being capable **of** being dealt with by classical electrodynamics.

In the case **of** displacements **of** electrons in the plane **of** the ring classical

electrodynamics is incapable **of** indicating any position **of** stabihty, and

Bohr finds the condition by introducing the quantum theory in the form

**of** the constant angular momentum (>^/27r) possessed by each electron in

whatever orbit it may be rotating.

It is assumed that the motions **of** the nuclei with respect to one

another are so slow that the state **of** motion **of** the electrons at any

moment will not differ sensibly from that calculated on the assumption

that the nuclei are at rest. This assumption is permissible on account

**of** the great mass **of** the nuclei compared with that **of** the electrons,

which means that the vibrations resulting from a displacement **of** the

nuclei are very slow compared with those resulting from a displacement

**of** the electrons.

Let us now imagine that, by the help **of** extraneous forces acting on

the nuclei, we slowly alter the distance between them. During this displacement

the radius **of** the ring **of** electrons will alter in consequence

**of** the alteration in the radial force due to the attraction **of** the nuclei

for the electrons. During this alteration we suppose that the angular

momentum **of** the electrons remains constant. If the distance apart **of**

the nuclei increases, the radius **of** the electron ring will likewise increase.

It can be shown, however, that the radius **of** the ring will increase at a

slower rate than does the distance between the nuclei. On account **of**

this difference in the rate the attraction on one **of** the nuclei due to the

ring will be greater than the repulsion from the other nucleus. The

work done during the displacement by the extraneous forces acting upon

the nuclei will therefore be positive, and the **system** will be stable for

this displacement. The same result will also hold in the case in which

the distance between the nuclei diminishes.

For a **system** consisting **of** a ring **of** electrons and two nuclei **of** unequal

charge the investigation becomes more complicated. During a

variation **of** the distance **of** the nuclei apart not only will the radius **of**

the electron ring vary, but also the ratio in which the plane **of** the ring