Question

1. (c) Powder diffraction experiment:

   The incident wavelength of a neutron beam is λ = 2.662 Å. The distance between adjacent atoms in a simple cubic crystal structure is 3.26 Å. Calculate the scattering angle of the 1st,

   2nd and 3rd diffraction maximum. Up to which order ’n’ can the diffraction peaks be observed?

Answer 1

We know the Bragg's diffraction condition

                                                         ; n = 1, 2 , 3.....................

Where d is inter-atomic separation, is the scattering angle, and is wavelength.

We can write,

                                      

According to the question,

                                       

So,

                                       

For first diffraction maxima i.e., n =1 :

                               

For second diffraction maxima i.e., n =2 :

                               

For third diffraction maxima i.e., n =3 :

                               

hence, only up to 2nd order, diffraction peaks could be observed.