Question

Solid A forms bcc lattice, Solid B forms fcc lattice. If the unit cell lengths (a) of A and B are 4 and 5 Å respectively, what is the ratio of the radii of A and B?

• A. \(5:4\sqrt{6}\)
• B. \(5:2\sqrt{6}\)
• C. \(4\sqrt{6}:5\)
• D. \(2\sqrt{6}:5\)

Hint:

For cubic lattices: bcc: \(4R = \sqrt{3}a\), fcc: \(4R = \sqrt{2}a\). Always use these formulas to find atomic radius from unit cell length.

Answer 1

The Correct Option is D

Step 1: bcc radius-edge relation.
For bcc, 4R = √3 a. With a_A = 4 Å, R_A = (√3/4) × 4 = √3 Å.

Step 2: fcc radius-edge relation.
For fcc, 4R = √2 a. With a_B = 5 Å, R_B = (√2/4) × 5 = (5√2)/4? Wait, correct: R_B = (√2/2) × 5 = (5√2)/2 Å.

Step 3: Forming the ratio R_A : R_B.
R_A : R_B = √3 : (5√2)/2 = (2√3) / (5√2) = (2√6) / 5.

Step 4: Conclusion.
Hence, the radii ratio is 2√6 : 5.