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The lattice spacing of the Davisson–Germer target, determined with X-ray crystallography, was measured to be a = 2.15 Å . Unlike X-ray crystallography in which X-rays penetrate the sample, in the original Davisson–Germer experiment, only the surface atoms interact with the incident electron beam. For the surface diffraction, the maximum intensity of the reflected electron beam is observed for scattering angles that satisfy the condition n λ = a sin φ (see [link] ). The first-order maximum (for n = 1 ) is measured at a scattering angle of φ 50 ° at Δ V 54 V , which gives the wavelength of the incident radiation as λ = ( 2.15 Å ) sin 50 ° = 1.64 Å . On the other hand, a 54-V potential accelerates the incident electrons to kinetic energies of K = 54 eV . Their momentum, calculated from [link] , is p = 2.478 × 10 −5 eV · s / m . When we substitute this result in [link] , the de Broglie wavelength is obtained as

λ = h p = 4.136 × 10 −15 eV · s 2.478 × 10 −5 eV · s / m = 1.67 Å .

The same result is obtained when we use K = 54 eV in [link] . The proximity of this theoretical result to the Davisson–Germer experimental value of λ = 1.64 Å is a convincing argument for the existence of de Broglie matter waves.

The graph shows the dependence of the intensity of the scattering beam on the scattering angle in degrees. The intensity degrees from 10 to 30 degrees, followed by a sharp increase and maximum at 50 degrees, and then reaches zero at 80 degrees.
The experimental results of electron diffraction on a nickel target for the accelerating potential in the electron gun of about Δ V = 54 V : The intensity maximum is registered at the scattering angle of about φ = 50 ° .
Figure shows the surface diffraction of a monochromatic electromagnetic wave on a crystalline lattice structure. The in-phase incident beams are reflected from atoms on the surface. Phi is the angle between the incident and the reflected beam, the in-plane distance between the atoms is a.
In the surface diffraction of a monochromatic electromagnetic wave on a crystalline lattice structure, the in-phase incident beams are reflected from atoms on the surface. A ray reflected from the left atom travels an additional distance D = a sin φ to the detector, where a is the lattice spacing. The reflected beams remain in-phase when D is an integer multiple of their wavelength λ . The intensity of the reflected waves has pronounced maxima for angles φ satisfying n λ = a sin φ .

Diffraction lines measured with low-energy electrons, such as those used in the Davisson–Germer experiment, are quite broad (see [link] ) because the incident electrons are scattered only from the surface. The resolution of diffraction images greatly improves when a higher-energy electron beam passes through a thin metal foil. This occurs because the diffraction image is created by scattering off many crystalline planes inside the volume, and the maxima produced in scattering at Bragg angles are sharp (see [link] ).

Picture A is a photograph of the diffraction pattern obtained in scattering on a crystalline solid with X-rays. Picture B is a photograph of the diffraction pattern obtained in scattering on a crystalline solid with electrons. Both pictures demonstrate diffracted spots symmetrically arranged around the central beam.
Diffraction patterns obtained in scattering on a crystalline solid: (a) with X-rays, and (b) with electrons. The observed pattern reflects the symmetry of the crystalline structure of the sample.

Since the work of Davisson and Germer, de Broglie’s hypothesis has been extensively tested with various experimental techniques, and the existence of de Broglie waves has been confirmed for numerous elementary particles. Neutrons have been used in scattering experiments to determine crystalline structures of solids from interference patterns formed by neutron matter waves. The neutron has zero charge and its mass is comparable with the mass of a positively charged proton. Both neutrons and protons can be seen as matter waves. Therefore, the property of being a matter wave is not specific to electrically charged particles but is true of all particles in motion. Matter waves of molecules as large as carbon C 60 have been measured. All physical objects, small or large, have an associated matter wave as long as they remain in motion. The universal character of de Broglie matter waves is firmly established.

Questions & Answers

how those weight effect a stable motion at equilibrium
Nonso Reply
how do I differentiate this equation- A sinwt with respect to t
Evans Reply
just use the chain rule : let u =wt , the dy/dt = dy/du × du/dt : wA × cos(wt)
Jerry
I see my message got garbled , anyway use the chain rule with u= wt , etc...
Jerry
de broglie wave equation
LoNE Reply
vy beautiful equation
chandrasekhar
what is electro statics
fitsum Reply
when you consider systems consisting of fixed charges
Sherly
Diagram of the derive rotational analog equation of v= u+at
Nnamnso Reply
what is carat
Arnulfo Reply
a unit of weight for precious stones and pearls, now equivalent to 200 milligrams.
LoNE
a science that deals with the composition, structure, and properties of substances and with the transformations that they undergo.
LoNE
what is chemistry
Mrs Reply
what chemistry ?
Abakar
where are the mcq
Fred Reply
ok
Giorgi
acids and bases
Navya
How does unpolarized light have electric vector randomly oriented in all directions.
Tanishq Reply
unpolarized light refers to a wave collection which has an equal distribution of electric field orientations for all directions
pro
In a grating, the angle of diffraction for second order maximum is 30°.When light of wavelength 5*10^-10cm is used. Calculate the number of lines per cm of the grating.
Micheal Reply
OK I can solve that for you using Bragg's equation 2dsin0over lander
ossy
state the law of gravity 6
cletus Reply
what is cathodic protection
Ebe Reply
its just a technique used for the protection of a metal from corrosion by making it cathode of an electrochemical cell.
akif
what is interferometer
Sonu Reply
what is interferometer
Abakar
Show that n1Sino1=n2Sino2
javan Reply
what's propagation
Vikas Reply
is it in context of waves?
Edgar
It is the manner of motion of the energy whether mechanical(requiring elastic medium)or electromagnetic(non interference with medium)
Edgar
Practice Key Terms 5

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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