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

Options

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

Answer

a

Explanation

`nlambda=2d sin theta`
`d=(lambda)/(2 sin theta)(` for `Ist ` order `) ...(1)`
`d=(a)/(sqrt(h^(2)+k^(2)+l^(2)))......(2)`
By eqn. `(1)` and `(2)`
`(lambda)/(2sintheta)=(a)/(sqrt(h^(2)+k^(2)+l^(2)))`
`sin theta=(lambda)/(2a)(h^(2)+k^(2)+l^(2))^(1//2)`