A system of physical chemistry - Index of

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A system of physical chemistry - Index of

io6 A SYSTEM OF PHYSICAL CHEMISTRY

configuration of the system in which the electrons, under the influence

of extraneous forces, rotate with the same angular momentum round

the nucleus in a ring of radius a where a = aao, « being greater than

unity. In this case we have P = - Pq (as follows from the definition of

a

potential energy given by equation (5))

; also on account of the con-

stancy of the angular momentum it follows that v = -V(i (compare equa-

tion (7)), and T = — ^Tq, for T involves the square of v and therefore

the square of a. It follows then that—

P + T = -Po + A-.To = (Po + To) + To (i - lY.

a a" \ a/

We see that the total energy (P + T) of the new configuration is

greater than the (Po + Tq) of the original configuration. The system

is therefore stable for the displacement considered, that is it will tend

to revert to the first configuration, for the first configuration corresponds

to a maximum value of W as defined previously.

The condition of stability which we have just been considering refers

to possible displacements of the electrons in the plane of the ring.

It

is necessary to consider the problem of stability in more detail however

before we take up the problem of actual atoms containing several

electrons.

Configuration and Stability in Systems Possessing one Nucleus.

Let us consider an electron of charge e and mass m moving in a

circular orbit of radius a with a velocity v, which is small compared

with the speed of light. Let us denote the radial force acting on the

electrons by -^ Fo ; Fo will be dependent in general upon a. The condition

of dynamical equilibrium gives—

mv e^

~ _2 ^0*

a a'^

Introducing the condition of universal constancy of the angular

momentum of the electron we have—

mva — hJ2ir.

From these relations we get— It^ ^ 2i:e^¥

a = —o ., -^ ';

and v =

/^Tr'^e'^mYo

and for the frequency of revolution—

cu = i^ir'^e^mYo^lh^.

h

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