Question

The metal potassium crystallizes in a body centered cubic unit cell with one atom per lattice point. When X-rays with λ = 1.937 Å are used, the second-order Bragg reflection from a set of parallel planes in a(n) potassium crystal is observed at an angle θ = 21.32°. If the spacing between these planes corresponds to the unit cell length (d = a), calculate the radius of a(n) potassium atom.

Answer 1

From Bragg's Law,

n$\lambda$ = 2d sin$\theta$

Where n = order of Bragg's reflection = 2

$\theta$ = angle = 21.32^o

$\lambda$ =1.937 $\AA$

So, 2*(1.937 $\AA$) = 2*d*sin(21.32)

d = 5.328$\AA$ = a= unit cell length

From BCC, relation between a and radius of K atom are:

d = 4*r / $\sqrt{3}$

5.328$\AA$ = 4*r / $\sqrt{3}$

r = 2.307$\AA$

Hence, radius of a potassium atom = 2.307$\AA$