AP EAMCET202120 Aug 2021Evening ShiftChemistrySolid StateActual
A metal crystallizes with a FCC -lattice, the edge of whose unit cell is xpm . The diameter of this metal atom would be p m .
Options
- A2   x
- Bx 2
- Cx 2
- D2 x
Correct answer
B. x 2
Step-by-step solution
In the face-centred unit cell, atoms are arranged at the corners and at centered of the face diagonal. Let radius of metal atom = r So, the distance AC = r + 2 r + r = 4 r The distance AD and CD = x Using the Pythagoras theorem, AC 2 = AD 2 + CD 2 AC 2 = x 2 + x 2 = 2 x 2 4 r 2 = 2 x 2 2 x = 4 r r = 2 x 4 = x 2 2 So, the diameter of this metal atom would be x 2 .