BHU PMT BHU PMT Solved Paper-2001

  • question_answer
    Pure silicon at 300 K has equal electrons\[{{n}_{e}}\], and Holes \[{{n}_{h}}\]concentration of\[1.5\times {{10}^{16}}/{{m}^{3}}\].Doping by Indium increases number of holes\[{{n}_{h}}\] to\[4.5\times {{10}^{22}}/{{m}^{3}}\,\,then\,\,{{n}_{h}}\]?doped in silicon will be:

    A)  \[3.0\times {{10}^{-19}}/{{m}^{3}}\]      

    B)  \[5\times {{10}^{9}}/{{m}^{3}}\]

    C)  \[4.5\times {{10}^{22}}/{{m}^{3}}\]                       

    D)  \[1.5\times {{10}^{16}}/{{m}^{3}}\]

    Correct Answer: B

    Solution :

    Key Idea: Law of mass-action can be used to achieve the required result. From law of mass-action                                                 \[n_{e}^{'}\,n_{h}^{'}=n_{i}^{2}\] \[\Rightarrow \]                               \[n_{e}^{'}=\frac{n_{i}^{2}}{{{n}_{h}}}\] Given, \[{{n}_{i}}=1.5\times {{10}^{16}}\,{{m}^{3}}\] \[\therefore \]                  \[n_{e}^{'}=\frac{{{\left( 1.5\times {{10}^{16}} \right)}^{2}}}{4.5\times {{10}^{22}}}\]                                                 \[n_{e}^{'}=5\times {{10}^{9}}/{{m}^{3}}\]


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