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# Davisson-germer Experiment - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

## Quick Facts

• Davisson-Germer Experiment is considered one of the most asked concept.

• 23 Questions around this concept.

## Solve by difficulty

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 $\dpi{100} d$ 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  $\dpi{100} N$ detected as a function of the detector position $\dpi{100} y$ ( $\dpi{100} y$ = 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 :

Match List - I (Experiment performed) with List - II (Phenomena discovered/ associated) and select the correct option from the options given below the lists :

 LIST I LIST II
 (a) Davisson and Germer Experiment (i) Wave nature of electrons (b) Millikan’s oil drop experiment (ii) Charge of an electron (c) Rutherford experiment (iii) Quantisation of energy levels (d) Franck -Hertz experiment (iv) Existence of nucleus

This question has statement 1 and statement 2 of the four choices given after the statements, choose the one that best describes the two statements

statement 1: Davisson – Germer experiment established the wave nature of electrons.

statement 2: It electrons have a wave nature, they can interfere and show diffraction.

What is the wavelength of the incident beam of electrons in the Davisson-Germer experiment if the accelerating potential is 54 V?

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In a Davisson Germer experiment, the distance between two adjacent crystal planes is $1.5 \AA$ . What is the angle of diffraction for constructive interference of electrons with a wavelength of $1.2 \AA$?

The wavelength of the X-rays is 0.071 nm which is diffracted by a plane of salt with 0.28 nm as the lattice constant. Determine the glancing angle for the second-order diffraction. Assume the value of the salt plane to be 110, and the given salt is rock salt.

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## Concepts Covered - 0

Davisson-Germer Experiment

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

• Electron gun: An electron gun comprising of a tungsten filament F was coated with barium oxide and heated through a low voltage power supply. It emits electrons when heated to a particular temperature. The electrons emitted by the electron gun are again accelerated to a particular velocity.
• Collimator: The accelerator is enclosed within a cylinder perforated with fine holes along its axis, these emitted electrons were made to pass through it. Its function is to render a narrow and straight (collimated) beam of electrons ready for acceleration.
•  Target: The target is a Nickel crystal. The beam produced from the cylinder is again made to fall on the surface of a nickel crystal. The crystal is placed such that it can be rotated about a fixed axis. Due to this, the electrons scatter in various directions.
• Detector: A detector is used to capture the scattered electrons from the Ni crystal. The beam of electrons produced has a certain amount of intensity which is measured by the electron detector and after it is connected to a sensitive galvanometer, it is then moved on a circular scale to record the current.

Observations of Davisson Germer experiment-

• The intensity of the scattered electron beam is measured for different values of angle of scattering ($\phi$)  by changing the $\phi$ (angle between the incident and the scattered electron beams).

These electrons formed a diffraction pattern. Thus the dual nature of matter was verified.

• The energy of the incident beam of electrons can be varied by changing the applied voltage to the electron gun.

Note-Intensity of a scattered beam of electrons is found to be maximum when the angle of scattering is $50^{o}$ 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.

• Bragg’s formula-

The path difference between electrons scattered from adjacent crystal planes is given by $\Delta x=2dsin\theta$

and  For constructive interference between the two scattered beams

$\Delta x=2d\sin \Theta = n\lambda$

where $d-distance\: between \: diffracting\: planes$

and  $\theta$  is the angle between the incident rays and the surface of the crystal

For the above figure $\phi =scattering \ angle$

As  $\theta+\phi+\theta=180^{o}$

So $\Theta = \frac{180-\phi }{2}$

As Intensity of a scattered beam of electrons is found to be maximum when the angle of scattering is $50^{o}$

So For $\phi =50^0$ we get  $\theta+50^{o}+\theta=180^{o}$

we get  $\theta = 65^{o}$

Co-relating Davisson Germer experiment and de Broglie relation-

According to de Broglie,

$\lambda _{e }= \frac{12.27}{\sqrt{V}}A^{\circ}$

and using V = 54 Volt we get $\lambda _e= 0.167 \ nm$

From Bragg’s formula we have $2d\sin \Theta = n\lambda$

The Lattice Spacing in Ni Crystal is given as d=0.092 nm.

And using $n=1 \ , \phi =50^0 \ and \ V=50 \ Volt$

we get $\lambda_e = 0.165 \ nm$

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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