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JEE Main Chemistry question

ChemistryThe Solid StateJEE Main

Not in JEE Main or NEET syllabus

A bcc lattice is made up of hollow spheres of . Spheres of solid are present inside the hollow spheres of . The radius of is half the radius of . The ratio of (total volume of spheres of unoccupied by in a unit cell) to (volume of unit cell) is . Find the value of .

Answer: 7

Solution

Let the radius of the hollow sphere be . In a bcc lattice the spheres touch along the body diagonal, so the edge length is and the unit cell volume is . Each bcc unit cell contains 2 spheres of (8 corners + 1 body centre),

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Question ID VK-141638