Flag AIIMS MBBS> A metallic element crystallises into a la...
question mark

A metallic element crystallises into a lattice containing a sequence of layers ABABAB.... Any packing of spheres leaves out voids in the lattice. Percentage of empty space (by volume) is
  1. 52%
  2. 48%
  3. 50%
  4. 74%

Abhishek Dogra , 6 Years ago
Grade 11
anser 1 Answers
Arun

Last Activity: 6 Years ago

Dear student
 
For a hcp unit cell, there are 6 atoms per unit cell. If r is the radius of the metal atoms, volume occupied by the metallic
Atoms 6 * 4/3 * π * r3 = 6 * 1.33 * 22/7 * r3 = 25.08 * r3
Geometrically it has been shown that the base area of hcp unit cell
= 6 * √3/4 * 4r2 and the height = 4r * √2/3
∴ Volume of the unit cell
= Area * height = 6 * √3/4 * 4r2 * 4r * \sqrt{\frac{2}{3}}= 33.94 r3
∴ Volume of the empty space of one unit cell
= 33.94 r3 – 25.08 r3 = 8.86 r3
∴ Percentage void = 8.816 r3/33.94 r3 * 100 = 26.1%
 
Regards
Arun
star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments