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Figure 36-46 is a graph of intensity versus angular positionfor the diffraction of an x-ray beam by a crystal. The horizontal scale is set bys=2.00.The beam consists of two wavelengths, and the spacing between the reflecting planes is0.94nm. What are the (a) shorter and (b) longer wavelengths in the beam?

Short Answer

Expert verified

(a) The shorter wavelength in the beam is,1=25pm .

(b) The longer wavelength in the beam is,2=38pm .

Step by step solution

01

Introduction of diffraction

Diffraction is a phenomena in which the interference or the bending of waves occurs around the corners of the opening or obstacle through or on which it strikes.

The diffraction formula is following,

苍位=2诲蝉颈苍胃=wavelengthd=spacing=bragg anglen=order of diffraction

02

Step 2: Identification of the given data

The spacing between reflecting plans is, d=0.94nm.

The bragg angle is, =2.00.

03

 Step 3: (a) Determination of the shorter Wavelength

As the graph is running from 0 degree to 2 degrees the shortest wavelength wave is present at around the 0.75 degrees.

So putting all the values we will get shortest wavelength

1=2dsin1

Substitute all the value in the above equation.

1=20.94nmsin0.751=0.025nm1=25pm

Hence the is the shortest wavelength is, 25pm.
04

(b) Determination of the longer wavelength

As the graph is running from 0 degree to 2 degrees the longest wavelength wave is present at around the 1.15 degrees.

So putting all the values we will get longest wavelength

2=2dsin2

Substitute all the value in the above equation.

2=20.94nmsin1.152=0.038nm2=38pm

Hence the longest wavelength is,38pm .

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