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Q14E

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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

A beam of electrons strikes a crystal at an angleθwith the atomic planes, reflects of many atomic planes below the surface, and then passes into a detector also making angleθwith the atomic planes. (a) If the minimumθgiving constructive interference is.35° What is the ratioλ/d, Where is the spacing between atomic planes? (b) At what other angles, if any, would constructive interference occur?

(a) The ratio of given minimum angle is λd=1.15.

(b) Here can notbe considered as2 . So this is an invalid value of thesin θ.As a result, the only integer that exists ism=1 .This is the smallest angle at which constructive interference was detected. As a result, constructive interference is not visible from any other angles.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Given data.

(a)

The angle of constructive interferenceθmin=35°.

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: Ratio between wavelength and spacing

Using equation(1) .

2dsinθ=mλ2sinθ=mλdλd=2sinθm

θmin is the minimum angle for the constructive interference, som=1 .

λd=2×sinθm=2×sin(35°)1=1.15

Therefore the ratio ofλd is 1.15in the spacing between the atomic planes.

Step 4: Condition for the constructive interference(b)

From Equation(1) the minimum value for sinθis1 .

So,

2dsin θ=mλsin θ=mλ2d1≥mλ2dm ≤2λd

Insertλd=1.15

m≤2λd≤21.15=1.74

Here m can notbe considered as 2. So this is an invalid value of the.sin θ

As a result, the only integer that exists ism=1 .

This is the smallest angle at which constructive interference was detected. As a result, constructive interference is not visible from any other angles.

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