Worksheet: X-Ray Diffraction

In this worksheet, we will practice calculating the angles of diffraction maxima and minima for diffraction using X-rays.

Q1:

Calcite crystals contain scattering planes separated by 0.300 nm. What is the angular separation between first and second-order diffraction maxima when X-rays of 0.130 nm wavelength are used?

Q2:

A first-order Bragg reflection maximum is observed when a monochromatic X-ray falls on a crystal at a 32.3 angle to a reflecting plane. What is the wavelength of this X-ray?

Q3:

The structure of the NaCl crystal forms reflecting planes 0.541 nm apart. What is the smallest angle, measured from these planes, at which X-ray diffraction can be observed, if X-rays of wavelength 0.085 nm are used?

Q4:

X-rays are produced by striking a target with a beam of electrons. Prior to striking the target, the electrons are accelerated by an electric field, increasing their potential energy by Δ𝑈=𝑒Δ𝑉, where 𝑒 is the charge of an electron and Δ𝑉 is the voltage of the electric field. If Δ𝑉=15,000volts, what is the minimum wavelength of the emitted radiation?

Q5:

On a certain crystal, a second-order X-ray diffraction maximum is observed at an angle of 26.0 relative to its surface, using an X-ray source of unknown wavelength. Additionally, when illuminated with a known wavelength of 0.106 nm, a second-order maximum is detected at 38.3.

Find the spacing between the reflecting planes.

Find the unknown wavelength.

Q6:

X-rays of wavelength 0.100 nm reflect off a crystal and a third-order maximum is recorded at a Bragg angle of 27.0. What is the spacing between the scattering planes in the crystal?

Q7:

An X-ray scattering experiment is performed on a crystal whose atoms form planes separated by 0.320 nm. Using an X-ray source of wavelength 0.496 nm, what is the angle at which the experimenter needs to illuminate the crystal to observe the first-order maximum?

Q8:

The first-order Bragg angle for a certain crystal is 14. What is the second-order angle?

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