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.
From Bragg's Law,
n = 2d sin
Where n = order of Bragg's reflection = 2
= angle = 21.32o
=1.937
So, 2*(1.937 ) = 2*d*sin(21.32)
d = 5.328 = a= unit cell length
From BCC, relation between a and radius of K atom are:
d = 4*r /
5.328 = 4*r /
r = 2.307
Hence, radius of a potassium atom = 2.307
The metal potassium crystallizes in a body centered cubic unit cell with one atom per lattice...
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