Question

In Davisson-Germer experiment, intensity was the maximum for accelerating voltage equal to
A. 44
B. 54
C. 64
D. 74

Answer 1

Hint: Recall Davisson-Germer experiment. Observe the effect of accelerating potential on the intensity of light diffracted from the metal surface. To answer this question, recall the phenomenon of interference of light and also the diffraction of light.

Complete step by step answer:
In the Davisson and Germer experiment, electrons are accelerated through a vacuum to a desired velocity by varying the accelerating potential. This accelerated beam of electrons is allowed to fall on a Nickel crystal where it scatters in all the directions. The intensity of scattered electrons is measured by varying the accelerating potential across the anode.
We know that Davisson and Germer varied the accelerating potential from 44 V to 68 V and observed the intensity pattern of scattered electrons at different scattering angles. The intensity of scattering was the maximum at the scattering angle \[50^\circ \]and the accelerating potential 54 V. We could see the peak in the intensity is the result of constructive interference of the electrons. We know that the intensity depends on the wavelength of scattering. At 54 V, the wavelength of scattering was,
\[\lambda = \dfrac{{1.228}}{{\sqrt V }}\]
Here, \[\lambda \] is the wavelength of light and V is the accelerating potential.
\[ \Rightarrow \lambda = \dfrac{{1.228}}{{\sqrt {54} }}\]
\[ \Rightarrow \lambda = 0.167\,{\text{nm}}\]

So, the correct answer is “Option B”.

Note:
To answer this question, students should know the interference of light, constructive interference and destructive interference. The constructive interference occurs when the maxima of the two interfering waves adds together to give maximum amplitude of the resultant wave. Since the Davisson-Germer experiment deals with diffraction, students should know that diffraction is the bending of light when it falls on the corners of an obstacle.