Question

Statement 1: Distance between nearest lattice points in BCC is greater than the same in FCC having same edge length.
Statement 2: FCC has greater packing efficiency than BCC.

• A. Statement-1 is true, statement-2 is true and statement-2 is the correct explanation for statement-1
• B. Statement-1 is true, statement-2 is true and statement-2 is not the correct explanation for statement-1
• C. Statement-1 is true, statement-2 is false
• D. Statement-1 is false, statement-2 is true

Answer 1

The correct option is B Statement-1 is true, statement-2 is true and statement-2 is not the correct explanation for statement-1

Lattice type	Number of lattice points/atoms per units cell	Nearest distance between lattice points	Maximum packing density	Example
Simple cubic	$\frac{1}{1}$	$a$	$\frac{\pi }{6}=52\%$	Phosphor
Body centered cubic	$\frac{2}{2}$	$\frac{a\sqrt{3}}{2}$	$\frac{\pi \sqrt{3}}{8}=86\%$	Tungsten
Face centered cubic	$\frac{4}{4}$	$\frac{a\sqrt{2}}{2}$	$\frac{\pi \sqrt{2}}{3}=74\%$	Aluminum
Diamond	$\frac{4}{8}$	$\frac{a\sqrt{2}}{2}$ Nearest distance between atoms: $\frac{a\sqrt{3}}{4}$	$\frac{\pi \sqrt{3}}{16}=34\%$	Silicon

From the above table it can be seen that distance between BCC lattice points is greater than distance between FCC lattice points.
Also the packing efficiency of FCC is more than BCC but it is not the explanation of the previous statement.