KVPY Sample Paper KVPY Stream-SX Model Paper-20

  • question_answer
    The edge length of unit cell of a metal having molecular weight \[75 g mo{{l}^{-1}}\] is \[5\,\overset{\text{o}}{\mathop{\text{A}}}\,\] which crystallizes in cubic lattice. If the density is 2g/cc then find the radius of metal atom. \[({{N}_{A}}=6\times 1{{0}^{23}}).\] Give the answer in pm.

    A) 217 pm

    B) 210 pm

    C) 220 pm

    D) 205 pm

    Correct Answer: A

    Solution :

    \[\rho =\frac{\operatorname{ZM}}{{{\operatorname{N}}_{A}}V}\]
    \[\operatorname{Z}=\frac{\rho {{\operatorname{N}}_{A}}V}{\operatorname{M}}=\frac{2\times 6\times {{10}^{23}}\times {{(5\times {{10}^{-8}})}^{3}}}{75}\]
    \[\operatorname{Z}=2,\] which represent \[bcc\]structure
    \[\therefore \text{ }r=\frac{\sqrt{3}}{4}a=\frac{\sqrt{3}}{4}\times 5=2.165\,\overset{\text{o}}{\mathop{\text{A}}}\,=216.5pm\approx 217pm\]


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