Q. If 'a' stands for the edge length of the cubic systems: simple cubic, body centred cubic and face centred cubic, then the ratio of radii of the spheres in these systems will be respectively
A) 1a : √3a : √2a
B) (1/2)a : (√3/4)a : (1/(2√2))a
C) (1/2)a : √3a : (1/√2)a
D) (1/2)a : (√3/2)a : (√2/2)a
Explanation
[Solution from source] Simple cubic: atoms touch along the edge, 2r = a, so r = a/2. bcc: they touch along the body diagonal, 4r = √3a, so r = (√3/4)a. fcc: they touch along the face diagonal, 4r = √2a, so r = a/(2√2). The (√3/2)a and (√2/2)a forms forget that the diagonal spans four radii. Answer (2).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.