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KVPY Sample Paper KVPY Stream-SX Model Paper-4

  • question_answer
    Percentage of free space in cubic close packed structure and in body centred packed structure are respectively

    A) 30% and 26%   

    B) 26% and 32%

    C) 32% and 48%   

    D) 48% and 26%

    Correct Answer: B

    Solution :

    [b]
    Packing % in lattice \[=\frac{\text{Total}\,\text{volume}\,\text{of}\,\text{spheres}}{\text{Volume}\,\text{of}\,\text{the}\,\text{unit}\,\text{cell}}\]
    Packing fraction of \[=\frac{\pi }{3\sqrt{2}}=0.74\]\[\Rightarrow \]\[74%\]
    % free space \[=100-\]packing fraction %
    % free space in ccp = 26%
    Packing fraction of bcc \[=\frac{\pi \sqrt{3}}{8}=0.68\]
    % free space in bcc = 32%


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