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Modern Physics
Found in: Page 134
Modern Physics

Modern Physics

Book edition 2nd Edition
Author(s) Randy Harris
Pages 633 pages
ISBN 9780805303087

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Short Answer

The setup depicted in Figure 4.6is used in a diffraction experiment using X-rays of0.26 nmwavelength. Constructive interference is noticed at angles of23.0oand,51.4o but none between. What is the spacing d of atomic planes?

The spacing of atomic planes is d=3.33×10-10m.

See the step by step solution

Step by Step Solution

Step 1: Given Data.

The angle of constructive interferenceθ1=23.0°.

The angle of constructive interferenceθ2=51.4°.

The wavelength of X-rays isλ=0.26×10-9m .

Step 2: Bragg's equation.

When there is constructive interference, Bragg's equation can be used to describe the relationship between the quantities.

2d sinθ =mλ…………(1)

Step 3: Constructive interference

Constructive interference occurs from two perspectives. Using the equation ,

2d sinθ1=mλ…………(2)2d sinθ2=(m+1)λ…………(3)

From equation

2dsinθ1=mλm =2dsinθ1λ

Step 4: The Atomic plane spacing.

Substitutem value in the equation.

2dsinθ2=(m+1)λ2dsinθ2=(2dsinθ1λ+1)λ2dsinθ2=2dsinθ1+λ2d(sinθ2-sinθ1) =λ

d =λ2(sinθ2-sinθ1)………………(4)

Therefore, using equation (4), we get the interplanar spacing such that,

d=0.26×10-9m2(sin(51.4°)sin(23.0°))=3.33×10-10 m

Therefore the atomic plane spacing is d=3.33×10-10m.

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