An X-ray beam of wavelength 0.48 x 10⁻¹⁰ m is used to get a Brag reflection from a crystal at an angle of 20° for the first-order maxima. What is the possible layer plane spacing which gives rise to this maximum? (0.70 x 10⁻¹⁰ m) 



Given:

Wavelength of X-rays beam = λ = 0.48 ｘ 10⁻¹⁰ m

Angle = θ = 20° 

Order of image = m = 1

To Find:


Crystal layer spacing = d = ?

Solution:


Using Braggs Equation

2 d sin θ = m λ

or 

d = `\frac {m λ}{ 2 sin θ}`

by putting values of m, θ, and λ

d = `\frac {1 ｘ 0.48 ｘ 10⁻¹⁰ m}{2 ｘ sin 20°}`

d = `\frac {0.48 ｘ 10⁻¹⁰ m}{2 ｘ 0.342}`

d = `\frac {0.48 ｘ 10⁻¹⁰ m}{0.684}`


by simplifying

d = 0.702ｘ 10⁻¹⁰ m

or

d = 0.70 ｘ 10⁻¹⁰ m  -------------------Ans


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