Question

The diffraction pattern of a certain metal was measured with X-ray radiation of a wavelength of 2.45 Å. The second-order Bragg diffraction peak was found at an angle 2θ of 50°. The d-spacing between the diffracting planes in the copper metal is _____

(sin 50° = 0.76, sin 25° = 0.42)

1. 3.25 Å
2. 5.83 Å
3. 0.41 Å
4. 4.2 Å

Answer 1

Correct Answer - Option 2 : 5.83 Å

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:

λ = 2.45 Å, n = 2, 2θ = 50.5° 

θ = 25°

From Bragg’s law:

⇒ 2 × d × sin 25° = 2 × 2.45 Å

⇒ \(d = \frac{{2.45}}{{\;\sin 25^\circ }} = 5.83Å\)