Q31 / 155 · WBJEE 2017 · Chemistry

In a close-packed body-centred cubic lattice of potassium, the correct relation between the atomic radius $(r)$ of potassium and the edge-length of the cube is

  • A
    $r=\frac{a}{\sqrt{2}}$
  • B
    $r=\frac{a}{\sqrt{3}}$
  • C
    $r=\frac{\sqrt{3}}{2} a$
  • Correct answer
    D
    $r=\frac{\sqrt{3}}{4} a$

Solution

$\because$ For be packing, $\sqrt{3} a=4 r \therefore r=\frac{\sqrt{3}}{4} \cdot a$ where $a=$ edge length $r=$ radius of lattice sphere

Hence, the correct answer is option: 'D'.

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