De - broglie waves theory, Physics

Q. Explain the wave nature of matter. 

De - Broglie Waves Theory

According to De - Broglie hypothesis, particles like electron, proton, neutron etc. show wavelike properties associated with them.

"All material particles in motion possess a wave character also".

These wave are called "Matter Waves" or "De Broglie Waves".

(1)  De - Broglie Wavelength of Matter Waves : A light wave of frequency v is associated with a photon of energy E is given by E = hv

(2)  Experimental Evidence of Matter Waves

(a)  Davission and Germer Experiment

(b)  G.P. Thomson Experiment

(a)  Demonstration of Matter Waves : Davission and Germe Experiment on Electron Diffraction - If material particles have a wave character, they are expected to show phenomena of interference and diffraction. In 1927, Davission and Germer demonstrated that a beam of electrons does suffer diffraction. The apparatus used in this experiment is shown in Fig. Electrons from a heated filament are accelerated through a variable potential v and emerge from the 'electron gun' G.

This electron beam falls normally on a nickel crystal C. The electrons are diffracted from the crystal in all directions. The intensity of the diffracted beam in different directions is measured by a Faraday cylinder connected to a galvanometer, which can be turned about an axis parallel to the incident beam. Thus any azimuth of the crystal can be presented to the plane defined by the beam entering the faraday cylinder.

First of all the accelerating potential V is given a low value and the crystal is turned at any arbitrary azimuth. The Faraday cylinder is moved to various position on the scale S and the galvanometer current at each position is noted. The current, which is a measure of the intensity of the diffracted beam, is plotted against the angle between the incident beam and the beam entering the cylinder. The observation are repeated for different accelerating potentials and the corresponding curves are drawn as shown in Fig.

It is seen that a 'bump' begins to appear in the curve for 44 volt electrons. With increasing potential the bump moves upwards and becomes most prominent in the curve for 54 volt electrons at 50°. At higher potentials the bump gradually disappears.

This, being in excellent agreement with the wavelength computed from de Broglie hypothesis, shows that electrons are wave like in some circumstances. Other fundamental particles like neutrons also show wave like characteristics.

Conception of Metter Trivial under ordinary situations

The wave nature of matter is not apparent to our daily observations. The reason is that in our daily life we come across macroscopic objects for which the de Broglie wavelength is extremely small. For example, the de Broglie wavelength of a bullet of mass 1 gm moving with a velocity of 105 cm / sec is given by

(b)  G.P. Thomson's Experiment

Experimental arrangement is shown in Fig. The electrons are produced from a heated filament F and accelerated through a high positive potential given to the anode A. the whole apparatus is kept highly evacuated.

The electron beam passes through a fine hole in a metal block B and falls on a gold foil G of thickness 10-8 meter. The electrons passing through the foil are received on a photographic plate P. The foil consists of very large numbers f microscopic crystal oriented at random. Therefore some of them are always at the correct angles to give rise to diffraction according to Bragg's formula.

Hence, on processing the plate, a central spot surrounded by a series of concentric diffraction rings is obtained. This shows that electron can get diffracted in some special conditions by a metal foil, which acts as diffracted in some special conditions by a metal foil, which act as diffracting elements for electrons.

Posted Date: 7/11/2012 3:07:43 AM | Location : United States

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