KVPY SX SB Exam 2013 Question Paper

Question : 56 of 120

Marks: +1, -0

If the angle of incidence of X-ray of wavelength 3Å which produces a second order diffracted beam from the (100) planes in a simple cubic lattice with interlayer spacing a = 6 Å is 30°, the angle of incidence that produces a first-order diffracted beam from the (200) planes is

15°
45°
30°
60°

Validate

Solution:

For the second-order diffraction from the plane (100)

d=\;{a}/{√{h^{2}+k^{2}+1^{2}}}=\;{a}/{√{1^{2}+0^{2}+0^{2}}}=6 Å ⇒ a=6 Å

For the first-order diffraction from the plane (200)

d=\;{a}/{√{h^{2}+k^{2}+l^{2}}}=\;{6}/{2}=3 Å

Using Bragg's equation:

n λ=2 d \sin θ

1 × 3=2 × 3 \sin θ

\sin θ=0.5 ⇒ θ=30

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