Which of the following relation is correct for first - order Bragg's diffraction?

Options

A. `sin theta = (2a)/(lambda) (h^(2) + k^(2) + l^(2))`
B. `sin theta = (2a)/(lambda) (h^(2) + k^(2) + l^(2))^(1//2)`
C. `sin theta = (lambda)/(2a) (h^(2) + k^(2) + l^(2))^(1//2)`
D. `sin theta = (lambda)/(2a) (h^(2) + k^(2) + l^(2))^(2)`

Answer

c

Explanation

`n lambda = 2d sin theta`
`d = (lambda)/(2 sin theta`…..(i)
`d= (a)/(sqrt(h^(2) + k^(2) l^(2))`….(ii)
comparing equation (i) and (ii) M
`(lambda)/(2 sin theta) = (a)/(sqrt(h^(2) + k^(2) + t^(2))`
`sin theta = (lambda)/(2d) (h^(2) + k^(2) + t^(2))^(1//2)`