The longest wavelength that can be analysed by a NaCl crystal of interplanar spacing 0.281 nm between its principal planes, in the first order, is:

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The longest wavelength that can be analysed by a NaCl crystal of interplanar spacing 0.281 nm between its principal planes, in the first order, is:

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AAI ATC Junior Executive 2018 Official Paper (Shift 3)

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0.654 nm
0.564 nm
0.969 nm
0.282 nm

Answer 1

Bragg’s Law:

Bragg's Law relates the angle θ (at which there is a maximum in diffracted intensity) to the wavelength of X-rays and the interlayer distance d between the planes of atoms/ions/molecules in the lattice.

bragg

Condition for constructive interference (maxima in the reflected).

nλ = 2d sinθ

λ = Wavelength of the X-ray

d = distance of crystal layers

θ = incident angle (the angle between the incident plane and the scattering plane)

n = integer (order)

This condition is known as Bragg’s law.

From the above equation,

\(λ = \frac {2d sin θ}{n}\)

In the first order (n = 1), the maximum wavelength possible is when sin θ is maximum;

Maximum value of sin θ = 1 ⇒ λ_max = 2d

Calculation:

Given first order ⇒ n = 1, d = 0.281 nm;

Now maximum wavelength will be

λ_max = 2d = 2 × 0.281 = 0.562 nm

∴ The longest wavelength that can be analysed = 0.562 nm

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The longest wavelength that can be analysed by a NaCl crystal of interplanar spacing 0.281 nm between its principal planes, in the first order, is:

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