A nucleus around which electrons orbit; electrons that can "jump" from one orbit to another absorbing or emitting energy- what a strange idea of an atom! Why should it be of such construction? Although the idea of the atom created by Rutherford and Bohr explained much it wasn't perfect.
Louis de Broglie was the one who found the solution. As you probably remember his conclusion about matter was that each particle except its corpuscular nature has also the wave nature. Also an electron circulating/rotating around a nucleus has a wave of some length. De Broglie suggested that orbits permitted for the electron are those, which circuit is equal to the exact multiple of the electron wavelength.
To understand it better let's take a look at the example of everyday life. I guess everybody has seen or even played a string instrument (a guitar, a violin, or a harp). Playing such instrument one induces different waves on strings. But most of these waves fade quickly. Only waves maintain, which at both ends have so called nodes (see fig.).
You should see your Delphi 4 forms or controls embedded in the form below.
The perimeters of the subsequent orbits are equal to:
(1)
where rn is the radius of the orbit. On the other hand the length of the orbit must be as long as some exact multiple of the electron wavelength:
(2)
Equating the formulas we get:
(3)
But we know that the wavelength of the wave of the electron is equal to:
(4)After placing (4) into (3) we get:
(5)
And transforming we get:
(6)
And that is how we achieve the assumption that Bohr made ad hoc! (We were dealing with this assumption on the previous page.)
