Question

The bragg's angle corresponding to the first order reflection from (111) plane in a crystal is 300 when x-ray of wavelength of 1.75 angstrom are used. Calculate the interplanar spacing and lattice parameter for the crystal. (n=1).

Answer 1

Answer:

INTER PLANAR SPACING ( d ) = 1 Å

Explanation:

★ X - RAYS ★

★ GIVEN ;

» Bragg's Angle For First order Reflection [ Glancing Angle ] ( ∅ ) = 300°

» Plane No. = 111

» Wavelength of X Rays ( Lambda ) =

1.75 Angstrom ( Å )

» Order of Diffraction ( n ) = 1

★ INTER PLANAR SPACING ( d ) = ???

_____ [ BY USING FORMULA ] ____

[ BRAGG'S EQUATION ]

$[2 \: \times \: d \: \times \: \sin( \alpha ) = n \: \times \: lambda \:]$

★ 2 × d × sin∅ = n × Lambda

» d = [ n × lambda ] / 2 × Sin∅

» d = [ 1 × 1.75 Å ] / 2 × Sin ( 300° )

» d = [ 175 × 10-¹² ] / 2 × (√3 / 2 )

» d = [ 175 × 10-¹² ] / √3

» d = [ 175 × 10-¹² ] / 1.75

» d = [ 100 × 10-¹² ]

★ INTER PLANAR SPACING ( d ) = 10^-10 m

------------------------ [ OR ] -----------------------

★ INTER PLANAR SPACING ( d ) = 1 Å

________________________________________

ANSWER :- Inter Planar Spacing between planes of Crystal Lattice having Glancing Angle 300° is ;

[ d = 10^-10 m ]