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  • An electron gun emits electrons at an accelerating voltage of 100 V. The beam of electrons is made to fall on a nickel crystal, and the scattered electrons are detected by a detector. If

An electron gun emits electrons at an accelerating voltage of 100 V. The beam of electrons is made to fall on a nickel crystal, and the scattered electrons are detected by a detector. If the intensity of the scattered beam of electrons is maximum when the angle of scattering is 45^{\circ} , what is the distance between the diffracting planes of the nickel crystal?

Option: 1

0.8 nm
 


Option: 2

0.7 nm
 


Option: 3

0.2 nm

 


Option: 4

0.5 nm


Answers (1)

best_answer

The Davisson-Germer experiment and the Frank Hertz experiment. The Davisson-Germer experiment demonstrated the wave nature of electrons through electron diffraction, and verified the de Broglie equation. The experimental setup included an electron gun, collimator, target, and detector. The scattered electrons produced a diffraction pattern and the dual nature of matter was verified. The Frank Hertz experiment verified the existence of discrete energy states in atoms, and the graph of collected current vs accelerating voltage showed a characteristic 4.9 \mathrm{~V} peak due to the ionization of mercury atoms. From Bragg's formula, 2 d \sin \theta=n \lambda. Here, \theta=45^{\circ}, n=1, and the wavelength of electrons can be calculated using the de Broglie equation, \lambda=h / p=h /(\sqrt{(2 m e V)}), where  h is Planck's constant, me is the mass of an electron, and \mathrm{V} is the accelerating voltage. Putting the values, we get \lambda=0.005 \mathrm{~nm} Solving for d, we get d=\lambda /(2 \sin \theta)=0.2 \mathrm{~nm}.

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