Wave length, of electron

According to this idea it ought to be possible to get interference with electrons, just as with light. This has proved to be the case, but the wave lengths of electrons are much shorter than those of visible light they are, in fact, about the same as the wave lengths of X-rays. 

The wave lengths of electrons are so short that it is not possible to perform experiments like Young s or Wiener s experiments with them. The method by which Davisson established the wave aspect of electrons was similar to that used... 

Davission s results on the wave lengths of electrons have been confirmed in an interesting way by G. P. Thomson, the son of J. J. Thomson, who showed that electrons are particles in 1897. 

In HREELS collective excitations are not possible due to the short wave length of electrons with a kinetic energy of 15eV, i.e. 0.32 nm, which is the range of the size of single molecules. The spectra of thin and thick film are therefore identical [27]. 

The theoretically obtained electron densities of ions may be used for the calculation of the so-called F curves, which give the effective reflecting power of the ion as a function of the angle of reflection and the wave-length of X-rays, and which are of use in the determination of crystal structures. It may be mentioned that the high maximum value of the electron density at the nucleus given by our calculations provides considerable justification for the method of determining crystal structures with the aid of the relative intensities of Laue spots produced by crystal planes with complicated indices. 

Three kinds of phenomenon play their part in the production of these band spectra, electronic changes within the molecule, vibration of the atoms in the molecule, and rotation of the molecule as a whole. The electronic processes give rise to emission or absorption in the visible and ultra-violet regions, the intra-atomic vibrations to bands in the short infra-red region at wave-lengths of the order of several /x, and the molecular rotations to bands in the far infra-red at wave-lengths of the order 100 /. ... 

The criterium that the mean free path should be larger than the superconducting coherence length must be met. This is a very strict condition that implies also that the impurity interband scattering rate yab should be very small yah (1/2 )(KB/ft)Tc. Therefore most of the metals are in the dirty limit where the interband impurity scattering mixes the electron wave functions of electrons on different spots on bare Fermi surfaces and it reduces the system to an effective single Fermi surface. 

The wave character of electrons was discovered experimentally by Davisson and Germer in 1927, and they found that the wave lengths were just equal to those given by de Broglie s theory. 

For electrons moving ten thousand miles per second, which is not very fast for electrons, he found the wave length to be about three-fifths of one one-thousand-millionth of an inch. According to this, the wave length for electrons moving only one foot per second would be about one-tenth of an inch, but there is no known way of experimenting with such slowly moving electrons. 

It has been shown rather recently by Dempster of Chicago that protons can be reflected from a single crystal and their wave length found just as with electrons. The wave lengths of protons are much smaller than those of electrons. 

The wave velocity u is equal to nl, where / is the wave length, so that we have l =u/n = uh/mC2. But C2 = uv so that / = h/mv. The product of the weight and the velocity of a particle is called its momentum, so that it appears that the wave length of the electron waves should be equal to Planck s constant divided by the momentum of the electron. h/m is equal to 1.13 for an electron, so that /=1.13A . This gives the wave length / in inches when v is expressed in inches per second. If v is ten thousand miles per second or one billion nine hundred million inches per second, we get the... 

In the same way for an electron or other particle of weight m moving with velocity v, the momentum mv is supposed to be equal to h/1 where 1 is the wave length of the electron waves. Hence mv = h/1 or 1 = h/mv. Also the frequency n is determined by the energy as for a photon. The energy is equal to... 

The momentum of a photon is equal to h/1 where h is Planck s constant and 1 the wave length of the photon. Hence if BE represents the momentum h/1 before the collision, and EC that lost, then the momentum lost is equal to (h/1) X EC/BE. But EC = 2EB sin 0/2 so that the momentum lost is equal to (2h/l) sin 0/2. If m denotes the weight or mass of the electron then its momentum is mv so that, since the momentum lost by the photon is equal to that gained by the electron we have... 

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