Question

Calcite crystals contain scattering planes separated by 0.30 nm. What is the angular separation between first and second-order diffraction maxima when X-rays of 0.130 nm wavelength are used?

Answer 1

The angular separation between the first and second-order diffraction maxima in a calcite crystal can be calculated using Bragg's Law formula. In this case, the X-ray wavelength is 0.130 nm and the spacing between scattering planes is 0.30 nm.

Step-by-step explanation:

When X-rays of a certain wavelength are diffracted by calcite crystals, they produce a series of diffraction maxima. These maxima occur at specific angles, which can be calculated using the Bragg’s Law formula:

nλ = 2dhk sin(θ)

Where n is the order of diffraction, λ is the wavelength of the X-rays, d is the spacing between the scattering planes, h and k are the Miller indices of the scattering plane, and θ is the angle of diffraction.

In this particular question, the wavelength of the X-rays is given as 0.130 nm and the spacing between the scattering planes is 0.30 nm. To find the angular separation between the first and second-order diffraction maxima, we can use the formula:
2d sin(θ₁) - 2d sin(θ₂)

Plugging in the values, we get:
2(0.30 nm) sin(θ₁) - 2(0.30 nm) sin(θ₂)