A beam of X-rays is constructively scattered in second order from the surface of the crystal at an angle of 30° and the spacing between layers of atoms in NACl crystal is 4.5 × 10-10 m. The wavelength of X-rays is ______

Question

Question

A beam of X-rays is constructively scattered in second order from the surface of the crystal at an angle of 30° and the spacing between layers of atoms in NACl crystal is 4.5 × 10-10 m. The wavelength of X-rays is ______

2.25 × 10^-10 m
1.25 × 10^-10 m
2.50 × 10^-10 m
1.50 × 10^-10 m

Answer 1

Concept:

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. 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)

Calculation:

Given:

d = 4.5 × 10-10 m, θ = 30°, n = 2

We know that,

nλ = 2d sin θ

∴ 2λ = 2 × 4.5 × 10-10 × sin 30°

λ = 2.25 × 10-10 m

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Question

A beam of X-rays is constructively scattered in second order from the surface of the crystal at an angle of 30° and the spacing between layers of atoms in NACl crystal is 4.5 × 10-10 m. The wavelength of X-rays is ______

Answer (Detailed Solution Below)

Detailed Solution

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