written 8.7 years ago by | • modified 8.7 years ago |
Find one wavelength of X-rays, if the lattice constant for copper is 3.615A0 . -
Mumbai university > FE > SEM 1 > Applied Physics 1
Marks: 7M
Year: May 2015
written 8.7 years ago by | • modified 8.7 years ago |
Find one wavelength of X-rays, if the lattice constant for copper is 3.615A0 . -
Mumbai university > FE > SEM 1 > Applied Physics 1
Marks: 7M
Year: May 2015
written 8.7 years ago by |
Bragg’s law-
Bragg emphasized on parallel planes & the set of planes are considered as Bragg’s planes. When X-rays are allowed to be incident on this planes, diffraction takes place & diffracted pattern gives information about the structure.
Let us consider parallel planes-
Let AB be my incident ray, which gets reflected along BC, another parallel beam gets incident along E, gets reflected along EF. Drop perpendicular from B such that it meets DE & EF along P & Q.
Now,
∆ = PE + EQ
∴ ∆ = BE.sin θ + BE.sin θ
∴ ∆ = 2 BE.sin θ
∴ ∆ = 2d.sin θ
But, ∆ = nλ ………here we consider constructive interference
∴ nλ = 2d.sinθ
This, is the required expression for Bragg's Law
Given:
n=1
θ=20
Miller indices is (2 1 2)
a = 3.615A or 3.615×10−10
To find: λ=?
Solution:
d=a√22+12+22
=3.615×10−10√9
=3.615×10−103
d= 1.205×10-10 m
By Bragg’s law-
nλ=2d.sinθ
λ=2×1.205×10−10sin20/1
λ=8.243×10−11m
λ=0.824A