GATE-2018 (24) :Wyllie – Time average equation

GATE-2008

Q36. An X-ray benm of wavelength(λ) =1.541 A⁰ is incident on a 

cubic crystal having lattice spacing of 4 A⁰. What will be its 2θ 

value (where θ is the glancing angle) on X- ray diffractogram?

A) 11.10 A⁰
         
B) 20.10 A⁰   
     
C) 22.20 A⁰  
                      
D) 22.20 A⁰

Solution:

Formula:

Bragg’s law===> 2*d* sinθ = n*λ-------------------(1)

wavelength (λ)= 1.541 A⁰

lattice spacing (d) = 4 A⁰

Angle between the incident angle and the surface of the crystal (θ) = ?

==> 2*d* sinθ= n*λ

==> sinθ = (n*λ) / (2*d)

==> sinθ = (1*1.541) / (2* 4)

==> sinθ = 0.1926

==> θ= sin^-1 (0.1926)

==> θ= 11.1045

Then, what is the value of 2θ (given problem)

==> 2θ= 2* 11.1045

==> 2θ=22.209