WAVE NATUREOF MATTERA PROJECT FILE
PREPARED BY
SUBMITTED TOTEJINDER SIR
ACKNOWLEDGEMENT
Primarily I would thank God for being able to complete this project with success. Then I would like to thank my physics teacher Tejinder Sir. , whose valuable guidance has been the ones that helped me patch this project and make it full proof success his suggestions and his instructions has served as the major contributor towards the completion of the project. Then I would like to thank my parents and friends who have helped me with their valuable suggestions and guidance has been helpful in various phases of the completion of the project. Last but not the least I would like to thank my classmates who have helped me a lot.
TABLE OF CONTENTS
DE BROGILE HYPOTHESIS AND WAVE NATURE OF MATTER
Page 4-5
DAVISSON AND GERMER EXPERIMENT
Page 5-8
THOMSON EXPERIMENT
Page 8-11
REFERENCES
Page 12
De Brogile Hypothesis and wave nature of matter In 1924, the French physicist Louis Victor de Broglie (1892-1987) put forward the bold hypothesis that moving particles of matter should display wave-like properties under suitable conditions. He reasoned that nature was symmetrical and that the two basic physical entities matter and energy, must have symmetrical character. If radiation shows dual aspects, so should matter.
De Broglie proposed that the wave length associated with a particle of momentum p is given as = h/p = h/mv
where m is the mass of the particle and v its speed. This equation is known as the de Broglie relation and the wavelength of the matter wave is called de Broglie wavelength. The dual aspect of matter is evident in the de Broglie relation. On the left hand side of equation is the attribute of a wave while on the right hand side the momentum p is a typical attribute of a particle. Plancks constant h relates the two attributes. Clearly is smaller for a heavier particle (large m) or more energetic particle (large v). In 1929, de Broglie was awarded the Nobel Prize in Physics for his discovery of the wave nature of electrons. A matter wave associated with a moving particle is represented by a wave packet as shown in the given figure:
DAVISSON AND GERMER EXPERIMENTThe wave nature of electrons was first experimentally verified by C.J. Davisson and L.H. Germer in 1927 and independently by G.P. Thomson, in 1928, who observed diffraction effects with beams of electrons scattered by crystals. Davisson and Thomson shared the Nobel Prize in 1937 for their experimental discovery of diffraction of electrons by crystals.The experimental arrangement used by Davisson and Germer consists of an electron gun which comprises of a tungsten filament F, coated with barium oxide and heated by a low voltage power supply (L.T. or battery).
Electrons emitted by the filament are accelerated to a desired velocity by applying suitable potential/voltage from a high voltage power supply (H.T. or battery). They are made to pass through a cylinder with fine holes along its axis, producing a fine collimated beam. The beam is made to fall on the surface of a nickel crystal. The electrons are scattered in alldirections by the atoms of the crystal. The intensity of the electron beam,scattered in a given direction, is measured by the electron detector (collector). The detector can be moved on a circular scale and is connected to a sensitive galvanometer, which records the current. The deflection of the galvanometer is proportional to the intensity of the electron beam entering the collector. The apparatus is enclosed in an evacuated chamber.By moving the detector on the circular scale at different positions, theintensity of the scattered electron beam is measured for different valuesof angle of scattering which is the angle between the incident and thescattered electron beams. The variation of the intensity (I) of the scattered electrons with the angle of scattering is obtained for different accelerating voltages.The experiment was performed by varying the accelerating voltagefrom 44 V to 68 V. It was noticed that a strong peak appeared in theintensity (I) of the scattered electron for an accelerating voltage of 54V ata scattering angle = 50The appearance of the peak in a particular direction is due to theconstructive interference of electrons scattered from different layers of the regularly spaced atoms of the crystals. From the electron diffractionmeasurements, the wavelength of matter waves was found to be 0.165 nm.The de Broglie wavelength associated with electrons, usingfor V = 54 V is given by = h /p = 1227/ (V)1/2 = 1227/(54)1/2 = 0.167 nmThus, there is an excellent agreement between the theoretical valueand the experimentally obtained value of de Broglie wavelength. Davisson Germer experiment thus strikingly confirms the wave nature of electrons and the de Broglie relation.Experiments with Fresnel diffraction and specularreflectionof neutral atoms confirm theapplicationto atoms of the de Broglie hypothesis. Further, recent experiments confirm the relations for molecules and even macromolecules, normally considered too large to undergo quantum mechanical effects. In 1999, a research team in Vienna demonstrated diffraction for molecules as large as fullerenes. The researchers calculated a De Broglie wavelength of the most probable C60velocityas 2.5pm.
THOMSON EXPERIMENTAfter the experiments on diffraction of electrons by C. J. Davisson and L. H. Germer, G. P. Thomson, the son of J. J. Thomson, also replicated the experiment on electron diffraction in 1927.Electrons from an electron source were accelerated towards a positive electrode into which a small hole was drilled. The resulting narrow beam of electrons was directed towards a thin, rolled foil of gold. After passing through the hole in the gold foil, the electron beam was received on a photographic plate placed perpendicular to the direction of the beam.
The diffraction pattern was in the form of continuous, alternate black and white rings as diffraction was due to the crystalline grains which were randomly oriented at all possible angles in the gold foil. The diffraction rings had narrowly defined radii and always seemed to occur in multiples i.e. circles of radii 2r,\,3r\, They were similar to the sharply defined principle maxima of the intensity pattern for -slits. Here the planes of atoms in the crystal act as slits. The radii of the different sets of rings were found to correspond precisely to the spacing of the various planes of atoms. Electrons were scattered at different angles from the atoms of crystallites and produced interference pattern with maxima corresponding to those angles satisfying the Bragg condition. In terms of the probabilistic interpretation of matter waves, the probability of finding an electron scattered at an angle \theta\, is exactly equal to computed intensity pattern of interfering waves associated with electron beam.The diffraction pattern due to polycrystalline material was similar to the powder diffraction pattern of X-rays having wavelength equal to the de Broglie wavelength of electrons. The wavelength of electrons was varied by changing the incident energy of the electrons, then diameters of the diffraction rings changed proportionately according to the Bragg's equation.When crystalline sample of aluminum was used, the diffraction pattern changed to spots lying around a ring-like structure.For Aluminum, the spacing between atomic planes..
According to the N-slit interference formula, the-order principle maximum occurs at angle. Braggs condition is . (Wavenumber for(i.e. the first-order principle maximum).From the experimental observations it is found thatdepends on the voltageas .For electron having mass, velocity, momentum, Kinetic Energythe relations are . .
Momentumis controlled by the voltage.Thusandboth are proportional to , (is the constant of proportionality)This is the relation between two intrinsic properties and Momentumof electrons. By substituting the values for the constantsand using the relation , Value of the proportionality constantcomes out to be aboutJ s,This value is quite close to the official value ofwhich is a universal constant of nature known as reduced Planck's constant and given by
Thus the de Broglies relation and his hypothesis of matter waves are verified.REFERENCESAbragam, A. (1988). Louis Victor Pierre Raymond de Broglie. 15 August 1892-19 March 1987. Biographical Memoirs of Fellows of the Royal Society, 34(0), pp.22-41.Greatians.com, (2016). PARTICLES AND WAVE. [online] Available at: http://www.greatians.com/physics/mass/particles%20wave.htm#MK.1.0 [Accessed 12 Jan. 2016].ncertbooks.prashanthellina.com, (2016). DUAL NATURE OF RADIATION AND MATTER. [online] Available at: http://ncertbooks.prashanthellina.com/class_12.Physics.PhysicsPartII/ch%2011.pdf [Accessed 12 Jan. 2016].pms.iitk.ernet.in/, (2016). Experimental Confirmation of Matter Waves. [online] Available at: http://pms.iitk.ernet.in/wiki/index.php/Experimental_Confirmation_of_Matter_Waves [Accessed 12 Jan. 2016].Rae, A. (1972). Lester H. Germer. Phys. Today, 25(1), p.93.Wikipedia, (2016). George Paget Thomson. [online] Available at: https://en.wikipedia.org/wiki/George_Paget_Thomson [Accessed 13 Jan. 2016].Wikipedia, (2016). Waveparticle duality. [online] Available at: https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality [Accessed 12 Jan. 2016].2
