Question

When a crystal surface is exposed to X-rays of 250 pm wave length, the first order reflection occurs at 30° The interplanar distance of the planes producing this reflection
IS
250 pm
125 pm
375 pm
500 pm
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Answer 1

Answer:

When a crystal surface is exposed to X-rays of 250 pm wave length, the first order reflection occurs at 30° The interplanar distance of the planes producing this reflection is 250 pm.

Explanation:

When an X-ray is an incident on a crystal surface, Brag's Law asserts that the angle of incidence θ, will reflect with the same angle of scattering θ, Constructive interference occurs when the path difference, d, is equal to a full number of wavelengths, n.

According to Bragg Equation:

nλ = 2d sinθ

Given n = First order reaction = 1

λ = 250 pm

θ = 30°

Find the interplanar distance of the planes producing this reflection means find value of d.

From Bragg.s law,

$\(d=\frac{n \lambda}{2 \sin \theta}=\frac{(1)(250 \mathrm{pm})}{(2)\left(\sin 30^{\circ}\right)}=250 \mathrm{pm}\)$

So, the interplanar distance of the planes producing this reflection is 20 pm.