Bragg's Law

Bragg's Law describes the diffraction of X-rays by a crystal lattice:

nλ = 2d sin θ

where:

* n is the order of diffraction (1, 2, 3, etc.)

* λ is the wavelength of the X-rays (in meters)

* d is the spacing between atomic layers (in meters)

* θ is the angle of diffraction (in radians)

Solving the Problem

1. Convert units:

* Wavelength (λ): 0.090 nm = 0.090 x 10⁻⁹ m

* Angle (θ): 15.2 degrees = 15.2 * (π/180) radians

2. Plug the values into Bragg's Law:

1 * (0.090 x 10⁻⁹ m) = 2 * d * sin (15.2 * (π/180))

3. Solve for d:

d = (0.090 x 10⁻⁹ m) / (2 * sin (15.2 * (π/180)))

d ≈ 1.72 x 10⁻¹⁰ m

Answer: The distance between atomic layers responsible for the first-order diffraction is approximately 1.72 x 10⁻¹⁰ meters (or 0.172 nm).