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Experimental Verification of Wave-particle Dualism: Davisson and Germer Experiment

The schematic diagram of the experimental arrangement is given in Figure 9.1. A collimated beam of electrons are scattered by a nickel target T capable of rotating about a vertical axis passing through the point of incidence. The scattered beam is received by Faraday’s cylinder F moving over a circular scale. Thus, the intensity of Scattered beam and angle 9 between the incident and scattered beam can be measured. The experiment was performed by varying the acceleration voltage of the electron and the angle 9 as shown in Figure 9.2.

FIGURE 9.2 Graph showing the variation of electron intensity with θ for different values    of accelerating voltage

 

In the experiment. the variation of the intensity of the scattered electron beam for different values of e are recorded for a particular value of the accelerating voltage. The experiment is repeated with different values of this voltage. Then a polar graph is drawn for each value of the voltage showing the intensity of the scattered electrons at different direction. At 40 V the graph is smooth. With increasing voltage the graph develops a peak at 50° and the peak becomes most pronounced for a voltage 54 v.

 

Bragg has demonstrated that when a beam of X-rays are scattered by a crystal, the maxima occur along the directions given by

 

2d sin θ = n’λ                                            . . . (1)

 

where d is the spacing between the crystal plane, n is the order of the maximum and θ is the angle between the crystal plane and the incident X-ray beam; called the glancing angle (figure 9.3)

 

For this experiment       d  =0.91  A ,n =1  and   =90-50/2 =650

 

Substituting these values in equation (1), we get wavelength

 

λ = 2 x 0.91 x sin 65° = 1.65 A.

 

In the Davisson and Germer experiment the maximum intensity occurs for an accelerating voltage 54 volts.

 

Thus, the de Broglie wavelength of electron may be obtained as

λ=h / p = h / √ 2 meV

= 6.625 x 10-34 /    √ 2 x 9.1 x 10 -31  x 1.6 x 10 -19 x 54 = 1.66 A

 

The agreement between the two values of wavelength is striking leading us to believe that the electrons have undergone diffraction through the crystal.