Question

The d spacing for the first-order X-ray ($\lambda$= 1.54 Å) diffraction event of metallic iron (fcc) at $2\theta= 20.2°$ is _______.Å. (round off to three decimal places)

Answer 1

Correct Answer: 4.39

To determine the d spacing for the first-order X-ray diffraction event, we use Bragg's Law, which is given by:

nλ=2d sinθ

 

Where:

• n is the order of diffraction, which is 1 for the first order.
• λ is the wavelength of the X-ray, λ=1.54 Å.
• d is the interplanar spacing, which we need to find.
• θ is the angle of diffraction, 20.2° in this case.

First, we convert the angle 2θ to θ:

θ=20.2°/2=10.1°

 

Now, plug the values into Bragg’s Law and solve for d:

1×1.54 Å=2d sin(10.1°)

 

d=1.54 Å/(2sin(10.1°))

 

Calculate sin(10.1°):

sin(10.1°)≈0.175

 

Substitute back to find d:

d=(1.54 Å)/(2×0.175)

 

d≈4.400 Å

 

Therefore, the d spacing is approximately 4.400 Å.