A criticism to the Rutherford's model of the atom

The Rydberg-Ritz formula

1. We think the Rutherford’s atom is like a micro-solar system in which the positive nucleus and negative electrons are bounded together because of the Coulomb electrostatic force (unlike-charges attract each other). We have to imagine that this attraction force, is well-balanced by another force because, if not, electrons impact against the nucleus. For this reason we imagine that electrons are not at rest, but turn around the nucleus in order to have a centrifugal force balancing the electrostatic force. This means also that electrons inside the atom are charged particles having a circular trajectory. In particular they are charged particles having a centripetal acceleration. This is in contrast with the Maxwell’s theory of Electromagnetism: charged accelerated particles irradiate energy (e.m. waves) in the surrounding space. From this point of view, if we admit that electrons lose energy emitting e.m. radiations while turning around the nucleus, we have to conclude that atoms can’t exist! Electrons lose energy ,so they slow down and spiral into the nucleus!

As a matter of fact, electrons of the atoms normally don’t emit radiation, atoms exist and we can observe them: perhaps the Rutherford’s model (son of the classical Physics) is too simple to explain a complex object like an atom.

2. Many experiments demonstrate that if we transfer energy to one atom (for example by heating) after a lapse of time the atom emits light. We can decompose this light in the component wavelengths by passing it through a glass prism. If we do this for the hydrogen atom we can see its spectrum of wavelengths (see fig 17.17 at page 355 on the Text Book). The spectrum is composed of discrete and well distanced lines distributed along the region of the ultraviolet visible and infrared e.m.waves. The position of the different lines in the spectrum can be described by a curious relationship discovered by Balmer and generalized by Rydberg and Ritz:

   Rydberg Ritz formula.   (1)

is the Rydberg’s constant, whose value is .

and are integer number satisfying the condition

When the formula reproduces the line spectrum emitted in the ultraviolet region.

When the formula reproduces the line spectrum emitted in the visible region.

When the formula reproduces the line spectrum emitted in the infrared region.

For instance, if we use by reversing the formula (1) we have

.

If we use we have

.

If we use we have

.

And so on…we can reproduce  the spectrum of light emitted by the hydrogen atom  shown on the Text-Book at page 355, and we can do this by inserting different integer numbers in the Rydberg-Ritz formula.

The Rutherford model is unable to explain why atoms emit line spectra instead of a continuum spectra: it feels like the atom is able to absorb and emit energy only with discrete values.

 A much deeper investigation was carried out by Niels Bohr in 1913.