KVPY Sample Paper KVPY Stream-SX Model Paper-22

  • question_answer
    Chromium metal crystallises with a body centred cubic lattice. The length of the unit edge is found to be 287 pm. Calculate the atomic radius. What would be the density of chromium in \[g/c{{m}^{3}}\]?

    A) 7.3

    B) 8.1

    C) 5.1

    D) 11.3

    Correct Answer: A

    Solution :

    In bcc unit cell, \[4r=\sqrt{3a}\]\[\Rightarrow \,\,r(Cr)=\frac{\sqrt{3}a}{4}=\frac{\sqrt{3}}{4}\times 287pm\]
    N = number of atoms per unit cell,
    M = molar mass
    \[{{a}^{3}}\] = volume of cubic unit cell,
    \[{{N}_{A}}\] = Avogadro's number
    For bcc Z = 2
    \[=\frac{2\times 52g}{6.023\times {{10}^{23}}}\times {{\left( \frac{1}{2.87\times {{10}^{-8}}cm} \right)}^{3}}\] \[=7.3g/c{{m}^{3}}\]

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