This document discusses using Bragg's law to calculate the wavelength range passing through an analyzer device. Bragg's law relates the wavelength of electromagnetic radiation to the diffraction angle for radiation scattering from a crystal. The document gives the first-order Bragg peak angle as 15.15 degrees for radiation with a wavelength of 0.149 nm. Using Bragg's law and taking the derivative with respect to angle, the document calculates the corresponding wavelength range of 1.439×10^-4 nm passing through an analyzer aperture of 0.015 degrees.

1. 1
A certain device for analyzing
electromagnetic radiation is
based on the Bragg scattering
of the radiation from a crystal.
For radiation of wavelength
0.149 nm, the first-order Bragg
peak appears centered at an
angle of 15.15◦
. The aperture of
the analyzer passes radiation
in the angular range of 0.015◦
.
What is the corresponding
range of wavelengths passing
through the analyzer?
Helping Tools
No.1
OR
No.2
No.3

2. 2
Solution
Using Bragg's Law,
2 sin --------------- (1)
for 1st order Bragg peak, 1
(1) 2 sin
differentiating w.r.t
2 cos
2 cos --------- (2)
n d
n
d
d
d
d
d d d
 
 




  
=
=
 =
=
 =

3. 3
,
2 sin
2sin
(2) 2( )cos
2sin
cot -------- (3)
Now
d d
d d
d d

 


  

   
=  =
 =
 =
9
4
4
4
Using
0.149 0.149 10
cot15.15 3.69
0.015
0.015
57.30
2.6178 10
in eq.(3), we get
0.149 3.69 2.6178 10
0.0001439 1.439 10
nm X m
d rad
X rad
d nmX X X
nm X nm



−
−
−
−
= =
=
= =
=
=
= =