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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 14

  • question_answer
    In a hexagonal closed packed system of crystals, assume that \[C=2\times \]distance between two close packed layers, and (r) is the radius of every sphere. The number of effective atoms and \[\left( \frac{C}{r} \right)\] ratio in this hcp unit cell are, respectively,

    A) \[8,\,24\sqrt{2}\,\,{{r}^{3}}\]         

    B) \[6,\,4\times \sqrt{\frac{2}{3}}\]          

    C)   \[12,\,24\,\,\sqrt{2}\,\,{{r}^{3}}\]       

    D)               \[12,4\times \sqrt{\frac{2}{3}}\]

    Correct Answer: B

    Solution :

    [b] Height \[(c)=2a\times \sqrt{\frac{2}{3}}\]     \[(\therefore \,\,a=2r)\] \[\therefore \,\,\,\left( \frac{c}{a} \right)=\frac{4r}{r}\times \sqrt{\frac{2}{3}}=4\times \sqrt{\frac{2}{3}}\] \[\therefore \,\,\,{{Z}_{eff}}\] in \[hcp=6\]


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