A system of physical chemistry - Index of

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A system of physical chemistry - Index of

RUTHERFORD-BOHR ATOM-MODEL 99

Combining thus with the equation (i) we obtain—

27r^W^E

If in these expressions we give t different values, we get a series of

values for W, w, and a, corresponding to a series of configurations of

the system, such configurations being stationary states in which there

is no radiation of energy, and in which the electron will remain as long

as the system is not disturbed from outside. We see that the value of

W is greatest if r has its smallest value, viz. unity. This will therefore

correspond to the most stable state of the system : i.e. it will correspond

to the binding of the electron for the removal of which the greatest

amount of energy is required. Substituting in the above expressions

T = I, and E = ^ = the charge on a single electron, and introducing

the experimental values, viz. 6? = 47 x lo-^", e/m = 5-31 x 10^",

h = 6-5 X ID '^^ we obtain:—

2a = II X 10-* cm. ; w = 6-2 X 10^^ per sec. ; W/e = 13 volt.

We see that these values are of the accepted order of magnitude for the

linear dimensions of the atoms, the optical frequencies, and the ionisa-

tion potentials respectively.

It is to be clearly borne in mind that the results so far obtained

rest on two main hypotheses :—

1. That the dynamical equilibrium of the systems in the stationary

states can be discussed by help of the ordinary electro-dynamics, whilst

the passage of the systems between different stationary states cannot be

treated on that basis.

2. That the latter process is followed by the emission of homogeneous

radiation, for which the relation between the frequency and the amount

of energy emitted is the one given by Planck's theory.

The next problem which Bohr takes up is to show that his theory

is capable of accounting for the line spectra of hydrogen.

If we consider the act of binding a free electron to a hydrogen

nucleus carrying a positive charge equivalent to the charge on a single

electron so that the electron finally rotates in one of the stationary

states, the energy radiated out in the formation of this stationary state

is given by equation (3), viz.— „. 2iT^me^

The amount of energy emitted by the passing of the electron from a

state where t = t^ to a state where t = T2 is consequently—

^2 ^1 h;^ Vt.v T- '1

The state corresponding to to is one in which the electron is closer to

the nucleus than in the state corresponding to t^ ; in short, ts is less

than Ti, and the linear dimension a of the atom is smaller when t = to

than when t = tj.

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