CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The packing efficiency of the face centered cubic (fcc), body centered cubic (bcc) and simple primitive cubic (sc) lattices follows the order :

A
fcc>bcc>sc
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
bcc>fcc>sc
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
sc>bcc>fcc
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
bcc>sc>fcc
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A fcc>bcc>sc
For simple cubic (sc):


Zeff for sc =1
So,

The total volume occupied by sphere V=1×43×πr3
Volume of the cube=a3=(2r)3
Packing efficiency (P.F)=1×43×πr3(2r)3×100%P.F=π×1006%=52.33%
For Face centered cubic (fcc) :

Here,
2×a=4ra=22×r

Zeff for FCC=4
So,

The total volume occupied by sphere V=4×43×πr3
Volume of the cube=a3=(22r)3
Packing efficiency (P.F)=4×43×πr3(22r)3×100%P.F=π×10032%74%


For Body centered cubic (bcc):

Here,
3×a=4ra=4r3

Zeff for BCC=2
So,

The total volume occupied by sphere V=2×43×πr3
Volume of the cube=a3=(4r3)3
Packing efficiency (P.F)=2×43×πr3(4r3)3×100%P.F=3π×1008%68%

Hence, the correct order is:
fcc>bcc>sc

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon