Question

Consider a one-dimensional wave of wavelength λ traveling through a one- dimensional lattice with lattice parameter a. Show that the waves scattered by each unit cell constructively interfere with each other only if 2a= nλ, where n is an integer.

Answer 1

In a one-dimensional lattice, waves scattered by each unit cell constructively interfere with each other only if 2a = nλ, where 'a' is the lattice parameter and 'n' is an integer.

Step-by-step explanation:

When X-rays are scattered by atoms in a crystal lattice, the waves can undergo constructive interference when the path length difference between the scattered waves is equal to an integer multiple of the wavelength. In the case of a one-dimensional wave traveling through a one-dimensional lattice, the waves scattered by each unit cell constructively interfere with each other only if the lattice parameter, a, is equal to half of the wavelength, λ, multiplied by an integer.