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  Wave Nature of Electrons

The Wave Nature of Electrons:

It has been made obvious that, when a substance is classified into finer and finer pieces, we reach molecules and atoms, and then we understand that the atoms comprise of electrons and nuclei. It has been explained that matter is a collection of ultra microscopic particles. Up to the 19th century, such particles were considered to move following Newtonian mechanics and Maxwellian electromagnetism.

Though, this point of view has become doubtful subsequent to the proposal of the Bohr model of the atomic structure (i.e., Bohr’s quantum theory).

On other hand, light had been believed to be electromagnetic waves.

Though, after the discovery of light quanta (i.e., photons), it was clarified that the light has wave nature at one time and particle nature at the other time. Thus, light has a type of duality.

The idea of de-Broglie wave nature or de-Broglie matter waves depend on the fact that light has both wave and particle nature. Therefore particle such as electron or proton can also be believed to be ‘particle’ with ‘wave nature’.

Einstein’s relations that connect the particle and wave aspects in light quanta is,

E = hν,    p = h/λ

would be satisfied for de-Broglie matter waves too. Hence the relations, shown in above equation are frequently termed as Einstein-de Broglie’s relations.

When we apply these relations to the situation of the Bohr model of the hydrogen atom, we can well recognize its possibility as follows. When we consider that the electron in a hydrogen atom moves at a constant speed all along a circular orbit around the nucleus (i.e., proton), the quantum condition in Bohr’s quantum theory is written as the equation shown below. By employing Einstein’s relation p = h/λ in this equation, the quantum condition is written as,

2πa = nλ,                 (n = 1, 2, 3 ...)

The above equation means that the circumference of the circular orbit of the electron should be an integral multiple of the wavelength of de Broglie wave. In another word, de-Broglie wave associating the motion of the electron must be continuous. Hence, we can easily understand the quantum situation which determines the stationary states by considering the stability of de Broglie waves (the figure is as shown below).

1041_wave nature.jpg

 

 

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