Question

An X-ray scattering experiment is performed on a crystal whose atoms form planes separated by 0.440 nm. Using an X-ray source of wavelength 0.548 nm, what is the angle (with respect to the planes in question) at which the experimenter needs to illuminate the crystal in order to observe a first-order maximum?

Answer 1

Using the Bragg's Law equation, and inserting the known values for the crystal spacing (d = 0.440 nm) and X-ray wavelength (λ = 0.548 nm), the angle of incidence (θ) can be calculated for observing a first-order maximum in an X-ray diffraction experiment.

Step-by-step explanation:

The student's question involves X-ray diffraction, which is an application of Bragg's Law in physics. To find the angle at which a first-order maximum occurs, Bragg's Law is used, which states that nλ = 2d sin θ, where n is the order of the maximum, λ is the wavelength of the X-rays, d is the spacing between the planes in the crystal, and θ is the angle of incidence with respect to the planes. For a first-order maximum (n=1), with X-rays of wavelength 0.548 nm and crystal planes separated by 0.440 nm, the equation simplifies to 0.548 nm = 2(0.440 nm) sin θ. Solving for θ gives us the angle required to observe the first-order maximum.