Question

The metal gold crystallizes in a face centered cubic unit cell with one atom per lattice point. When X-rays with λ = 1.436 Å are used, the second-order Bragg reflection from a set of parallel planes in a(n) gold crystal is observed at an angle θ = 20.62°. If the spacing between these planes corresponds to the unit cell length (d = a), calculate the radius of a(n) gold atom.

Answer 1

Answer:

 r =  1.45 Å

Explanation:

given,

λ = 1.436 Å

θ = 20.62°

d = a

n = 2

metal gold crystallizes in a face centered cubic unit cell

Radius of the gold atom = ?

using Bragg's Law

 n λ = 2 d sin θ

 2 x 1.436 Å = 2 a sin 20.62°

 a = 4.077 Å

We know relation of radius for face centered cubic unit cell

 $a = \dfrac{4r}{\sqrt{2}}$

 $4.077= \dfrac{4\times r}{\sqrt{2}}$

 r =  1.45 Å

the radius of a(n) gold atom. is equal to 1.45 Å