In an XRD analysis using a wavelength of 154 pm, a crystalline sample of a layered VO(PO₄)(H₂O) structure gave peaks at 24.2°, 36.3°, and 48.4°. What is likely to be the value of the distance between the layers? A) 731 pm B) 367 pm C) 103 pm D) 188 pm E) 55.1 pm

Question

Quizplus · Accepted Answer

The distance between the layers (d-spacing) can be calculated using the Bragg equation:
nλ = 2d sin(θ)
where n is the order of the reflection (n = 1 in this case), λ is the wavelength of the X-rays, θ is the Bragg angle (in radians), and d is the distance between the layers.

Converting the wavelength to meters:
λ = 154 pm = 1.54 x 10^-10 m

Converting the Bragg angles to radians:
θ1 = 24.2° = 0.422 radians
θ2 = 36.3° = 0.633 radians
θ3 = 48.4° = 0.845 radians

Using the first peak (n=1, θ=0.422 radians):
d = λ/(2sin(θ1)) = 731 pm

Therefore, the best choice is A) 731 pm, which is the likely value of the distance between the layers of the crystalline sample.

In an XRD Analysis Using a Wavelength of 154 Pm