Question

The spacing between atomic planes in a crystal is 0.130nm. 15.0 keV x rays are diffracted by this crystal.

Part A

What is the angle of first-order diffraction?

Theta =

Part B

What is the angle of second-order diffraction?

Theta =

Answer 1

Equation for diffraction

2 d cos?_m=m ?

Here d = 0.13 nm = 0.13 x 10^-9 m

E = h c / ?

? = h c / E = 6.63 x 10^-34 x 3 x 10^8 / ( 15 x 10^3 x 1.6 x 10^-19 ) = 8.287 x 10^-11 m

Part A

m = 1

2 d cos?_m=m ?

cos?₁ = m ? / 2 d = 1 x  8.287 x 10^-11 / ( 2 x 0.13 x 10^-9 ) = 0.3187

?₁ = arccos(0.3187) = 71.41 ^o

---------------------------------------------------------------------------------------------------------------------------------------

Part B

m = 2

cos?₂ = m ? / 2 d = 2 x  8.287 x 10^-11 / ( 2 x 0.13 x 10^-9 ) = 0.6374

?₂ = arccos(0.6375) = 50.39 ^o

------------------------------------------------------------------------------------------------------------------

angle of first-order diffraction = 71.41 ^o

angle of second-order diffraction = 50.39 ^o