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Davisson-Germer Experiment is considered one of the most asked concept.
5 Questions around this concept.
Question is based on the following paragraph.
Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see figure).
Question : In an experiment, electrons are made to pass through a narrow slit of width comparable to their de Broglie wavelength. They are detected on a screen at a distance D from the slit.
Which of the following graphs can be expected to represent the number of electrons detected as a function of the detector position ( = 0 corresponds to the middle of the slit)?
Match List - I (Fundamental Experiment) with List - II (its conclusion) and select the correct option from the choices given below the list :
Davisson and Germer Experiment, for the first time, proved the wave nature of electrons through electron diffraction and also verified the de Broglie equation.
In this experiment, we will study the scattering of electrons by a Ni crystal.
The experimental setup for the Davisson and Germer experiment is enclosed within a vacuum chamber.
The experimental arrangement of the Davisson Germer experiment consists of the following main parts
Observations of Davisson Germer experiment-
These electrons formed a diffraction pattern. Thus the dual nature of matter was verified.
Note-Intensity of a scattered beam of electrons is found to be maximum when the angle of scattering is and the accelerating potential is 54 V.
i.e we could see a strong peak in the intensity. This peak was the result of the constructive interference of the scattered electrons.
The intensity of the scattered electrons is not continuous. It shows a maximum and a minimum value corresponding to the maxima and the minima of a diffraction pattern produced by X-rays.
Galvanometer in Davisson Germer Experiment-
The detector is connected to a sensitive galvanometer to measure the small values of current due to scattered beam of electrons.
The path difference between electrons scattered from adjacent crystal planes is given by
and For constructive interference between the two scattered beams
where
and is the angle between the incident rays and the surface of the crystal
For the above figure
As
So
As Intensity of a scattered beam of electrons is found to be maximum when the angle of scattering is
So For we get
we get
Co-relating Davisson Germer experiment and de Broglie relation-
According to de Broglie,
and using V = 54 Volt we get
From Bragg’s formula we have
The Lattice Spacing in Ni Crystal is given as d=0.092 nm.
And using
we get
Therefore the experimental results are in a close agreement with the theoretical values got from the de Broglie equation.
Thus Davisson and Germer Experiment verify the de Broglie equation.
Frank Hertz Experiment-
This experiment is the first experimental verification of the existence of discrete energy states in atoms.
For this experiment, the graph of Collected current Vs Accelerating Voltage is given below
Frank and Hertz had proposed that the 4.9 V characteristic of their experiments was due to the ionization of mercury atoms by collisions with the flying electrons emitted at the cathode.
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