Question

In the cubic lattic given below, the three distances between the atoms A-B,A-C, and A-G are, respectively.

A. `a,sqrt(2)a,sqrt(3)a`
B. `a,sqrt(3)a,sqrt(2)a`
C. `(a)/(2),(a)/sqrt(2),(sqrt(3)a)/(2)`
D. `a,(sqrt(3)a)/(2),sqrt(2)a`

Answer 1

i. Edge length =AB=AD=BC=CD=a
ii. `AC=sqrt((AB^(2))+(BC)^(2))=sqrt(a^(2)+a^(2))=sqrt(2)a`
iii. `AG=sqrt((AC^(2))+(CG)^(2))=sqrt(2a^(2)+a^(2))=sqrt(3)a`