question_answer

Consider an electron \[(m=9.1\times {{10}^{-31}}kg)\] confined by electrical forces to move between two rigid walls separated by \[1.0\times {{10}^{-9}}\]metre, which is about five atomic diameters. The quantised energy value for the lowest stationary state is [ISM Dhanbad 1994]

A)            \[12\times {{10}^{-20}}Joule\]                                         

B)            \[6.0\times {{10}^{-20}}Joule\]

C)            \[6.0\times {{10}^{-18}}Joule\]                                        

D)            6 Joule

Correct Answer: B

Solution :

           It will form a stationary wave                    \[\lambda =2l=2\times {{10}^{-9}}m\]                    \[\Rightarrow \lambda =\frac{h}{\sqrt{2mE}}\]                    \[\Rightarrow E=\frac{{{h}^{2}}}{2m{{\lambda }^{2}}}=6\times {{10}^{-20}}J\]