The radius of an atom is 300pm, if it crystallizes in a face centered cubic lattice, the length of the edge of

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Q. The radius of an atom is 300pm, if it crystallizes in a face centered cubic lattice, the length of the edge of the unit cell is

(a) 488.5pm

(b) 848.5pm

(d) 484.5pm

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Step 1. In a face-centred cubic (fcc) lattice, atoms touch along the face diagonal, so $4r = \sqrt{2}\,a$ .

Step 2. Rearranging for the edge length: $a = \dfrac{4r}{\sqrt{2}} = 2\sqrt{2}\,r$ . …

Q.The radius of an atom is 300pm, if it crystallizes in a face centered cubic lattice, the length of the edge of the unit cell is