3.4 Theory of dualism as proposed by the french prince de broglie  (Page 2/2)

Table 1.1. The Three Basic families of elementary particles.

1.3.1. CONDITIONS FOR EXHIBITING WAVE-PARTICLE DUALITY-DEGENERACY TEMPERATURE.

We know from diffraction experiment and double slit Young’s Interference Experiment [Appendix XV] that when the limit of Geometrical Optics is reached, ray optics is replaced by wave optics. That is when the wavelength of light(λ) is much smaller than the aperture dimension ‘a ‘ light is not diffracted and Ray Optics is applicable. When the aperture dimension is comparable to the wavelength then diffraction starts taking place.

What this means is that light shows its particle nature when aperture is very wide but light exhibits wave nature when aperture is of comparable dimension.

In a similar manner when particle’s de Broglie wavelength is comparable to the spacing between the scatterers then wave nature of the particle is exhibited.

In quantitative terms: (mv ² )/2 = (3/2)kT

Therefore mv = √(3mkT) = p (linear momentum);

Therefore the condition for wave particle duality is:

λ = h/√(3mkT) ≈ a ( spacing between the scatterers);

At T ≤ T 0 = h 2 /(3mka 2 ) 1.12

= Degeneracy Temperature where we have wave-particle duality ;

For solids and liquids a = 2 to 3 Angstrom

Therefore an electron which has mass of the order of 10 ^-30 Kg will manifest wave nature below degeneracy temperature T ₀ = 265× 10 ³ K. That is an electron in a solid/liquid will exhibit wave nature for all temperature at which matter can exist in solid/liquid phase. Therefore Electron Microscope operates at Room Temperature.

If electron is replaced by an hydrogen atom and scatterer spacing is of the same order then T ₀ is 50Kelvin. Therefore wave nature of hydrogen atom will show up below 50K . Super fluids of helium are a result of wave particle duality. Therefore we have to achieve quantum liquids where atoms exhibit wave nature and this can be achieved only at liquid helium temperature or lower.

1.4. ELECTRON DIFFRACTION BY CRYSTALS ( THE FINAL VINDICATION OF MATTER WAVES)

In 1927 an accident in Bell Telephone Lab (founded by Alexander Graham Bell [Appendix XVI ] ) went a long way in establishing the revolutionary concept of matter waves.

In 1909 Earnest Rutherford [Appendix XVII ] was carrying a systematic research on the atomic structure. In the process he bombarded a thin gold foil with Alpha Rays. He recorded the deflection of the Alpha particles. While studying the deflection pattern he concluded that most of the mass of the Atom was concentrated in the nucleus of the Atom and electrons were orbiting the nucleus in much the same way as planets were orbiting the Sun. Thus he proposed the Planetary Model of Atom.

In 1927 like Rutherford, Josef Davisson and Lester Hailburt Germer(in USA) [Appendix XVIII ] were bombarding Nickel foil with electron beam. Initially Nickel was a poly crystal and there was nothing noteworthy in the scattering pattern and the scattering pattern was no way correlated to the accelerating voltage in the electron gun. But then an accident occurred and air leaked into the apparatus. Nickel got oxidized and to reduce it to elemental form it was baked in an oven. In the course of the heating cycle , Nickel had transformed into a large single crystal structure and this periodic structure diffracted the electrons in much the same way as X-Ray had been diffracted in X-Ray Crystallography developed by Bragg [Appendix XIX] . The apparatus , the scattering pattern and its dependence on voltage is shown in Figure(1.7) [ This experiment is described in Modern Physics by Richtmeyer, Kennard&Cooper ,1969, McGraw Hill ]

Figure 1.9. The Davisson-Germer Experimental Appratus and the resulting scattering pattern and its dependence on voltage.

From the diffraction pattern, the wavelength of the incident waves could be determined if the lattice constant was known. Also detailed crystalline structure could be determined.

Since lattice constant , wavelength of electrons and wavelength of X-Ray are of the same order, of the order of Angstrom, hence Crystallography can be carried out as easily with electrons as they are carried out with X-Ray.

For X-Ray crystallography, Lau and Bragg Father and Son Group received Nobel Prizes in 1914 and 1915 respectively.

For confirming the existence of Matter Waves by electron crystallography, Davisson(USA) , Germer(USA) and G.P.Thomson (England) [Appendix XX] received the Nobel Prize in 1937. G. P. Thomson, son of J. J. Thomson the discoverer of electron, independently verified the wave-particle duality of electron.

In 1931 Stern and Collaborators carried out the matter wave diffraction using slow He atoms targeted on LiF crystals. Again Lau diffraction pattern was obtained.

In 1988, Keith et al (Physical Review Letter, Vol. 61, pp. 1580) repeated the experiment with slow Na atoms(11e,11p&12n) targeted on Gold Membrane with two well separated slits. This gave the interference pattern as obtained in Young’s double slit interference experiment.

In 90’s neutron interferometer has been achieved. The neutron beam is passed through well separated slits and after the passage through the slit it is allowed to fall on a screen where incident neutrons are counted at different points of incidence in transverse direction. We obtain alternating dark and bright fringe pattern as obtained in Young’s double slit experiment on light. Here dark implies low count and bright implies high count. If one of the slits is closed we get uniform pattern. The dark and bright fringes disappear.

In 1666 Issac Newton [Appendix XXI] had proposed the corpuscular nature of light. Only in 1801 when Thomas Young demonstrated the phenomena of Interference in monochromatic light that wave nature of light was accepted and established.

In 1927 the diffraction pattern of electrons finally established the wave nature of matter with definiteness.