The spacing of one set of crystal planes in NaCl table salt) is d = 0.282 nm. A monochromatic beam of x-rays produces a Bragg maximum when its glancing angle with these planes θ = 7° .  Assuming this is a first-order maximum (m=1). Find the wavelength of the X-rays.  (0.069 nm)



Given:


Crystal plane spacing = d = 0.282 ｘ 10⁻¹⁰nm

Angle = Î¸ = 7° 

Order of image = m = 1


To Find:


The wavelength of x-ray = Î» = ?

Solution:


Using Braggs Equation

2 d sin Î¸ = m Î»

or 

λ = `\frac {2d sin θ}{m}`

by putting values of m, θ, and d

λ = `\frac {2 ｘ0.282 ｘ 10⁻¹⁰ m ｘ sin 7°}{1}`

λ = 564 ｘ 10⁻¹⁰ m ｘ 0.122 


by simplifying

λ = 0.6881 ｘ 10⁻¹⁰ m

or

λ = 0.06881 ｘ 10⁻⁹ m

or

λ = 0.069 nm  -------------------Ans


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