Question

Which of the following patterns has a void fraction of 0.26?
A. $AAAA......$
B. $AB\,AB\,AB...$
C. $ABC\,ABC\,ABC...$
D. $ABCCBAABC....$

Answer 1

Hint: According to the question, we have the given void fraction. First, we have to calculate the packing fraction of the layering pattern. Then with the help of packing fraction, we can find the Packing Efficiency of the particles inside the lattice.

Complete step-by-step answer: It has given that void fraction of layering pattern = 0.26. So, packing fraction of layering pattern = 1 - 0.26 = 0.74 , packing fraction may have a negative or positive sign. The negative sign of the packing fraction means that the isotopic mass is less than the mass number of the isotope.
Now, we have the formula of Packing Efficiency:
Packing efficiency is defined as the percentage of space occupied by constituent particles packed inside the lattice.
Packing Efficiency= $100 \times packing\,fraction$
Packing Efficiency = $100 \times 0.74 = 74\% $
But we know packing efficiency of face centered cubic lattice (fcc ) is $74\% $ .
 Hence the layering pattern is face centered cubic lattice.
And, we all know the arrangement of FCC is $ABCCBAABC....$

Hence, the correct option is (D.) $ABCCBAABC....$

Note:Metal atoms normally pack themselves in a nearby course of action to shape the most grounded metallic bond conceivable. In nature, a few pressing game plans are conceivable, including the face-focused cubic course of action.