Question

The longest wavelength X-ray that can undergo Bragg diffraction in a crystal for a given family of planes of spacing d is
1. \(\frac{d}{4}\)
2. \(\frac{d}{2}\)
3. d
4. 2d

Answer 1

Correct Answer - Option 4 : 2d

Concept:

Bragg’s Law states that when an X-ray beam are allowed to scatter through a crystalline surface, its angle of incidence θ will reflect with some angle of scattering θ. And when the path difference d is equal to a whole number n, of wavelength.

It can be represented as

2dsinθ  =nλ

Calculation:

Given

For longest wavelength, θ = 90°, n = 1

From Bragg’s law:

2d sin θ = nλ

Thus, 2d = λ