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NEET Sample Paper NEET Sample Test Paper-77

  • question_answer
    The space occupied in different packing?s is called packing fraction. \[\operatorname{Packing} fraction =\,\,\frac{total\,\,volume\,\,of\,\,sphere}{volume\,\,of\,\,the\,\,unit\,\,cell}\] Fraction of total volume occupied by atoms in a simple cubic unit cell is

    A)  \[\frac{\pi }{2}\]                                   

    B)  \[\frac{\sqrt{3\,\pi }}{8}\]

    C)  \[\frac{\sqrt{2\,\pi }}{6}\]                     

    D)  \[\frac{\pi }{6}\]

    Correct Answer: D

    Solution :

    In simple cubic arrangement, number of atoms \[=1\] \[\operatorname{a}=2r\] Packing fraction \[=\,\,\,\,\frac{Volume\text{ }occupied\text{ }by\text{ }one\text{ }atom}{Volume\,\,of\,\,unit\,\,cell}\] \[=\,\,\,\frac{\frac{4}{3}\pi {{r}^{3}}\,}{{{a}^{3}}}\frac{\frac{4}{3}\pi {{r}^{3}}}{{{(2r)}^{3}}}\,\,=\,\,\frac{\pi }{6}\]


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