Davisson Germer experiment

This experiment provide the experimental confirmation of de Broglie hypothesis

• F = Filament, made of tungsten.
• The electrons are accelerated from F on heating it by a low tension battery.
• G = An anode containing a fine hole.
• C = Nickel crystal, the electrons are strike on this crystal and then scattered in all possible directions.
• D = Detector, which can be rotated on a circular scale S, and this detector is used to measure the intensity of electrons scattered by C.
• φ = Angle between the incident electron beam on crystal and the scattered direction of electron.
• If we plot a graph between φ and I (intensity of scattered electron beam by C) at different V.

Conclusions

• I depends on φ.
• There is always a bump or kink occurs in the curve at φ = 50°.
• As the value of accelerating voltage V increases the size of bump increases.
• The bump become maximum at V = 54 volt.
• On further increasing the value of V, bump starts to decrease.
• According to de Broglie

or      λ = 1.67 Å

• From Bragg’s law

           2d sin θ = nλ

• Here n = order of diffraction, d = inter-planar distance, and θ = glancing angle of diffraction
• For X-ray analysis Ni works as plane diffraction grating
• d₁₁₁ = 0.91 Å for Ni crystal
• Since diffraction angle φ = 50°
• Therefore glancing angle θ = (180 ー50) / 2 = 65°

∴    2 × 0.91 sin 65° = 1 × λ

or    λ = 1.65 Å

• The excellent agreement between the two results for wavelengths (λ) confirms de-Broglie hypothesis for electrons.
• It means the electron beam of energy 54eV at 50° angle posses strong diffraction, which shows the wave nature and Ni crystal works as diffraction grating.