Saved Bookmarks
| 1. |
Calculatepackingefficinecy in thecrystal of body -centredcubic (bcc) structure. |
|
Answer» Solution :Body -centred cubic (bcc) structure: In thisunit cell, THEREARE 8 atoms at 8 cornersand one atom atthe body centre . `therefore` Total NUMBER of atoms `= 8 xx (1)/(8) + 1 = 1 + 1 = 2` If a is the edgelengthof cubicunit cell and r is theradius of an atom them, in bcc unitcell `r =(sqrt(3))/(4) xxa` VOLUMEOF unit cell `=a^(3) = ((4)/(sqrt(3))xx r)^(3) = (64)/(3sqrt(3))r^(3)` Volumeof 1 atom `= (4)/(3)pir^(3)` `therefore` Packing fraction `=("Volumeoccupiedby 2atoms")/("Volume of unit cell")` `=(2xx(4)/(5)pir^(3))/((64)/(3sqrt(3))r^(3))` `= (sqrt(3)pi)/(8)` `=(sqrt(3) xx 3.142 )/(8)` ` = 0.68` `therefore` Packingefficinecy `= 0.68 xx 10= 68%` `therefore` %of voidspace= 100-68 = 32% . |
|