question_answer

Directions: Questions No. 90 are 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).             Electrons accelerated by potential V are diffracted from a crystal. If \[d=1\overset{o}{\mathop{A}}\,\] and\[i={{30}^{o}}\], V should be about (\[h=6.6\times {{10}^{-34}}Js\],\[{{m}_{e}}=9.1\times {{10}^{-31}}kg,\,e=1.6\times {{10}^{-19}}C\])     AIEEE  Solved  Paper-2007  

A) 500 V    

B) 1000 V  

C) 2000 V  

D) 50 V

Correct Answer: D

Solution :

For constructive interference, path difference \[=n\lambda \]                 From the given figure, path difference = MP+PN = 2d cos i \[\therefore \]  \[2d\,\cos i=n\lambda \Rightarrow \lambda =\frac{\sqrt{3}}{n}\overset{o}{\mathop{A}}\,\]                 Also \[\lambda =\sqrt{\frac{150}{V}}\overset{o}{\mathop{A}}\,\] \[\therefore \,\,\,{{\left( \frac{\sqrt{3}}{n} \right)}^{2}}=\frac{150}{V}\Rightarrow V=50\,{{n}^{2}}\] For n = 1, V = 50 volt