X-ray beam of wavelength undergoes a first order reflection from a crystal when its angle of incident to a crystal face is 26.5°, and an X-ray beam of wavelength 0.097 nm undergoes a third order reflection when its angle of incidence to that face is 60°. Assuming that the two beams reflect from the same family of planes, calculate (a) the interplanar spacing of the planes and (b) wavelength. (Ans: (a) 0.168 nm, (b) 0.150 nm)



Data Given:

For 1st order reflection:

Angle = θ₁ = 26.5° 
Wavelength  = λ₁ = ?
n₁ = 1

For 3rd order reflection:

Angle = θ₂ = 60° 
Wavelength  = λ₂ = 0.097 nm = 0.097 ｘ 10⁻⁹ m
n₂ = 3


To Find:


(a) Crystal Interplanar spacing = d = ?

(b) Wavelength of 1st order reflection = λ₁ = ?


Solution:


(a) Crystal Interplanar spacing = d = ?


Using Braggs Equation (3rd order reflection)

2 d sin θ₂ = m₂ λ₂

or 

d = m₂λ₂2sinθ₂

by putting the corresponding values 

d = 3ｘ0.097ｘ10⁻⁹m2sin60°

d = 0.291ｘ10⁻⁹m2ｘ0.866


by simplifying

d = 0.168 ｘ 10⁻⁹ m

or

d = 0.168 nm ---------------Ans.(1)


(b) Wavelength of 1st order reflection = λ₁ = ?

Again using the brag's formula (for 1st Order reflection)

2d sin θ₁ = m₁ λ₁

or 

λ₁ = 2dsinθ₁m₁


by putting the corresponding values

λ₁ = 2ｘ0.168ｘ10⁻⁹mｘsin26.5°1

λ₁ = 0.336  ｘ 10⁻⁹ m ｘ 0.446

λ = 0.149856 ｘ 10⁻⁹ m 

or

λ₁ = 0.15 nm -----------------------Ans (2)



************************************

Shortcut Links For 


1. Website for School and College Level Physics   
2. Website for School and College Level Mathematics  
3. Website for Single National Curriculum Pakistan - All Subjects Notes 

© 2022-Onwards by Academic Skills and Knowledge (ASK)     

Note:  Write me in the comment box below for any query and also Share this information with your class-fellows and friends.