V.6 No 1

11

On excited state of orbital electron

In passing from the complex solution to that real, if the initial expression for the exciting force (60) contains only a real part, (77) will transform to the following appearance:

where

Then, taking

yield

where

The yielded solutions (80) show, the electron’s excited orbiting is a complicated oscillation dependent on the frequency of oscillations in a stationary orbit and on the frequency of affecting force. With it, the periodicity of oscillation that provides the atom’s maximal radiation at the excitation frequency will take place only at the frequency _E multiple to  _e . This is just the resonance of which many authors wrote. But it considerably differs from the known type of resonances that appear in linear elastic systems with which we usually compare the atom’s excitation. The difference is first of all such. As we could see from modelling equations, the electron is affected by an orbiting field whose frequency depends both on the frequency of external excitation and on the frequency of electron’s stationary orbiting in its main orbit. And, as we will see below, this gives other patterns of oscillation process as Bohr and his followers thought.

Fig. 10. The scheme to calculate the relation between the inertial reference frame and the frame of electron moving in the stationary orbit

But before we, basing on (80), yield the final solution, we have to pass to the inertial reference frame, Fig. 7. It will be easy, given in accordance with Fig. 10

With the relation (81), the solution (80) describes excited motion of electron in a weak external electric time-variable field.