chemistry bragg law

Question

The lattice parameter of silver, an fcc structure, is 408.6 pm. An X-ray beam produces a strong reflection from the (111) planes at 2ϴ = 38.2º. What is the wavelength of the X-rays?

Answer 1

The edge length of its unit cell is 408.6 pm or

408.6×10^-10 cm

a = d x (h² + k² + l²)^1/2 where hkl = (111) are Miller indices

d = 408.6×10^-10 cm / \sqrt(3)

using formula,

d = 0.5 x lambda / sin (19.1)

lambda = 154.38 * 10^-10 cm