In a certain X-rays diffraction experiment, the first-order image is observed at an angle of 5° for a crystal plane spacing of 2.8 x 10⁻¹⁰ m. What is the wavelength of X-rays used? (0.49 X 10⁻¹⁰ m) 



Given:

Angle = θ = 5° 

Order of spectrum = m = 2

Crystal plane spacing = d = 2.8 ｘ 10⁻¹⁰ m/lines

To Find:


Wavelength = λ = ?

Solution:


Using Braggs Equation

2 d sin θ = m λ

or 

λ = `\frac {2d sin θ}{m}`

by putting values of m, θ, and d

λ = `\frac {2 ｘ2.8 ｘ 10⁻¹⁰ m ｘ sin 5°}{1}`

λ = 5.6 ｘ 10⁻¹⁰ｘ 0.087 m


by simplifying

λ = 0.4881 ｘ 10⁻¹⁰ m

or

λ = 0.49 ｘ 10⁻¹⁰ m  -------------------Ans


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