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  • The Davisson-Germer experiment involves the diffraction of electrons by a crystal lattice. The figure below shows a typical diffraction pattern obtained in the experiment. <p dir="

The Davisson-Germer experiment involves the diffraction of electrons by a crystal lattice. The figure below shows a typical diffraction pattern obtained in the experiment.

If the lattice spacing of the nickel crystal is 0.092 nm, what is the angle of diffraction for the first order peak when the accelerating voltage of the electrons is 54 V?

 

Option: 1

26.4^{\circ}


Option: 2

65^{\circ}


Option: 3

36.4^{\circ}


Option: 4

41.2^{\circ}


Answers (1)

best_answer

In the Davisson-Germer experiment, a beam of electrons is accelerated towards a nickel crystal. The electrons are diffracted by the crystal lattice and produce a diffraction pattern on a screen behind the crystal.

The diffraction pattern consists of a series of peaks that correspond to different angles of diffraction. The angle of diffraction is given by:

\sin \theta=\frac{n \lambda}{2 d}

where \theta is the angle of diffraction, n is the order of the diffraction peak, \lambda is the de Broglie wavelength of the electrons, and d is the lattice spacing of the crystal.

The de Broglie wavelength of an electron is given by:

\lambda=\frac{h}{p}

where h is Planck's constant and p is the momentum of the electron. The momentum of an electron is given by:

p=\sqrt{2 m_e E}

where m_e is the mass of an electron and E is the kinetic energy.

Substituting the given values, we get:

\lambda=\frac{h}{\sqrt{2 m_e E}}=\frac{6.626 \times 10^{-34} \mathrm{~J} \mathrm{~s}}{\sqrt{2 \times 9.109 \times 10^{-31} \mathrm{~kg} \times 54 \mathrm{~V}}}=0.167 \mathrm{~nm}

Substituting the values into the formula for the angle of diffraction, we get:

\sin \theta=\frac{1 \times 0.167 \mathrm{~nm}}{2 \times 0.092 \mathrm{~nm}}=0.9087

Taking the inverse sine of both sides, we get:


\theta=\sin ^{-1} 0.9087=65.32

where \theta is the angle between the incident rays and the surface of the crystal And also \theta is the angle of diffraction
(Now For\phi= scattering \, \, angle

As \theta+\phi+\theta=180^{\circ}

So \phi=180-2 \theta

So \phi=50^0 \text { ) }

 

Posted by

Suraj Bhandari

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