Which one of the following statements is not correct?

  • A
    Schottky defect in ionic solids does not change the density of the crystal
  • B
    Packing efficiency is the percentage of total space filled by the particles
  • C
    In body centered cubic unit cell,the relationship between atomic radius $(r)$ and the edge length $(a)$ is,$r = \frac{\sqrt{3}}{4} a$
  • D
    Photovoltaic cell is used for conversion of light energy into electrical energy

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$A$ body-centred cubic $(BCC)$ element of density $10.3 \ g \ cm^{-3}$ has a cell edge of $314 \ pm$. Calculate the atomic mass of the element. Also, Lithium borohydride crystallizes in an orthorhombic system with four molecules per unit cell. The unit cell dimensions are $a = 6.8 \ \mathring{A}$, $b = 4.4 \ \mathring{A}$, and $c = 7.2 \ \mathring{A}$. If the molar mass is $21.76 \ g \ mol^{-1}$, calculate the density of the crystal.

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An element crystallizes in a body-centred cubic $(BCC)$ structure with an edge length of $400 \ pm$. Calculate the interatomic distance in the crystal. Additionally, if an atom has a radius of $300 \ pm$ and crystallizes in a face-centred cubic $(FCC)$ lattice, calculate the distance between the nearest neighbours.

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Which of the following statement(s) is (are) correct?

Atoms of metals $x$,$y$,and $z$ form face-centred cubic $(fcc)$ unit cell of edge length $L_x$,body-centred cubic $(bcc)$ unit cell of edge length $L_y$,and simple cubic unit cell of edge length $L_z$,respectively. If $r_z = \frac{\sqrt{3}}{2} r_y$; $r_y = \frac{8}{\sqrt{3}} r_x$; $M_z = \frac{3}{2} M_y$ and $M_z = 3 M_x$,then the correct statement$(s)$ is (are) [Given: $M_x$,$M_y$,and $M_z$ are molar masses of metals $x$,$y$,and $z$,respectively. $r_x$,$r_y$,and $r_z$ are atomic radii of metals $x$,$y$,and $z$,respectively.]
$(A)$ Packing efficiency of unit cell of $x >$ Packing efficiency of unit cell of $y >$ Packing efficiency of unit cell of $z$
$(B)$ $L_y > L_z$
$(C)$ $L_x > L_y$
$(D)$ Density of $x >$ Density of $y$

Calculate the number of atoms present in $1.58 \ g$ of a metal that forms a $bcc$ structure,given that $\varrho \times a^3 = 1.58 \times 10^{-22} \ g$.

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