question_answer

A potential barrier of \[0.3\] Volt exists across a p-n junction. The depletion region is 1 pm wide. The intensity of electric field in this region is E. If electron with speed \[5\times {{10}^{5}}m/s\] approaches this p-n junction from n-side, what will be its speed V on entering the p-side?     

A)  \[V=12\times {{10}^{5}}m/s\]

B)  \[V=1\times {{10}^{4}}m/s\]

C)   \[V=3.8\times {{10}^{5}}m/s\]

D)  \[V=1.6\times {{10}^{4}}m/s\]

Correct Answer: C

Solution :

[c] The intensity of electric field \[E=\frac{V}{d}=\frac{0.3}{1\times {{10}^{-6}}}=3\times {{10}^{5}}\,V/m\]             The electric field retarded the electron. The retardation            \[a=\frac{Ee}{m}\] The speed of the electron on entering p-side          \[{{v}^{2}}={{u}^{2}}-2as={{u}^{2}}-2\frac{eE}{m}.d\] \[={{(5\times {{10}^{5}})}^{2}}-\frac{2\times 1.6\times {{10}^{-19}}\times 3\times {{10}^{5}}}{9.1\times {{10}^{-31}}}\times (1\times {{10}^{-6}})\] \[=3.8\times {{10}^{5}}\,m/s\]