X-rays of wavelength 0.15 nm are observed to undergo a first order reflection at a Bragg angle of 13.3° from a quartz (SiO₂) crystal. What is the interplanar spacing of the reflecting planes in the crystal? (Ans: 0.326 nm)



Data Given:


Wavelength of X-ray = λ = 0.15 nm = 0.15 ｘ 10⁻⁹ m

Angle = θ = 13.3° 

Order of reflection = m = 1


To Find:


Crystal interplanar spacing = d = ?

Solution:


Using Braggs Equation

2 d sin θ = m λ

or 

d = `\frac {m λ}{2 sin θ}`

by putting the corresponding values 

d = `\frac {1 ｘ 0.15 ｘ 10⁻⁹ m}{2 sin 13.3°}`

d = `\frac {0.15 ｘ 10⁻⁹ m}{2 ｘ 0.230}`


by simplifying

d = 0.326 ｘ 10⁻⁹ m

or

d = 0.326 nm ---------------Ans.


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