JEE Main & Advanced Chemistry The Solid State / ठोस प्रावस्था Question Bank Mathematical analysis of cubic system and Bragg's equation

  • question_answer
    Potassium has a \[bcc\] structure with nearest neighbour distance \[4.52\,\,{AA}.\] Its atomic weight is 39. Its density (in \[kg\,\,{{m}^{-3}}\])  will be        [AIIMS 1991]

    A) 454        

    B) 804

    C) 852        

    D) 908

    Correct Answer: D

    Solution :

    For bcc,\[d=\frac{\sqrt{3}}{2}a\]or \[a=\frac{2d}{\sqrt{3}}=\frac{2\times 4.52}{1.732}=5.219\text{{ }\!\!\mathrm{\AA}\!\!\text{ }}=522\,pm\]            \[\rho =\frac{Z\times M}{{{a}^{3}}\times {{N}_{0}}\times {{10}^{-30}}}\]\[=\frac{2\times 39}{{{(522)}^{3}}\times (6.023\times {{10}^{23}})\times {{10}^{-30}}}\]                                    \[=0.91\,g/c{{m}^{3}}=910\,kg\,{{m}^{-3}}\]


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