X-ray diffraction methods MCQs With Answer

X-ray Diffraction (XRD) methods MCQs With Answer are designed to help M. Pharm students master core and advanced aspects of crystalline solid characterization within Modern Pharmaceutical Analytical Techniques. This quiz focuses on fundamental theory (Bragg’s law, Miller indices, selection rules), instrumentation (sources, optics, detectors, geometries), data quality (counting statistics, step size, profile functions), and applied pharmaceutics (polymorph identification, preferred orientation control, quantitative phase analysis, and amorphous content determination). You will also encounter practical considerations such as fluorescence mitigation, internal standards, and modeling line broadening via crystallite size and microstrain. These MCQs emphasize both conceptual understanding and problem-solving relevant to polymorph screening, stability studies, and regulatory-quality diffraction data generation in pharmaceutical R&D and QC.

Q1. Which equation defines the condition for constructive interference in X-ray diffraction from crystal planes?

• nλ = 2d sin θ
• nλ = d sin 2θ
• λ = d/2θ
• d = λ cos θ

Correct Answer: nλ = 2d sin θ

Q2. Using Cu Kα radiation (λ = 1.5406 Å), what is the d-spacing for a peak at 2θ = 20°?

• 4.43 Å
• 2.21 Å
• 3.13 Å
• 6.11 Å

Correct Answer: 4.43 Å

Q3. Which is a key advantage of powder XRD for pharmaceutical solids screening?

• It requires large single crystals for analysis
• It measures only amorphous halos and not crystalline peaks
• It works on microcrystalline powders without the need for single crystals
• It directly provides full atomic coordinates from a single scan in all cases

Correct Answer: It works on microcrystalline powders without the need for single crystals

Q4. For a face-centered cubic (FCC) lattice, which reflection condition is correct for allowed peaks in powder XRD?

• h, k, l all odd or all even are allowed; mixed parity is absent
• Only h + k + l = even is allowed
• Only h = k = l is allowed
• All hkl are allowed without restriction

Correct Answer: h, k, l all odd or all even are allowed; mixed parity is absent

Q5. In a Bragg–Brentano θ–2θ powder diffractometer, which statement best describes the scan geometry?

• The incident angle equals θ and the detector moves at 2θ to satisfy focusing
• The sample and detector both remain stationary while the tube moves
• The detector stays still at a fixed 2θ while only the sample rotates
• The incident angle remains 90° to maximize scattering

Correct Answer: The incident angle equals θ and the detector moves at 2θ to satisfy focusing

Q6. Why is a Ni filter commonly used with a Cu anode source in powder XRD?

• To increase the intensity of Cu Kβ radiation
• To selectively absorb Cu Kβ radiation and reduce spectral overlap
• To convert Kα to Kβ radiation via fluorescence
• To narrow the divergence of the incident beam

Correct Answer: To selectively absorb Cu Kβ radiation and reduce spectral overlap

Q7. Using the Scherrer equation (instrumental broadening negligible), estimate the crystallite size for a peak at 2θ = 40° with FWHM = 0.20° (in 2θ), K = 0.9, λ = 1.5406 Å.

• 4.2 nm
• 42 nm
• 420 nm
• 0.42 nm

Correct Answer: 42 nm

Q8. Which sample preparation approach best minimizes preferred orientation for plate-like pharmaceutical crystals?

• Strong front-loading with pressing to a smooth surface
• Back-loading the sample holder and spinning the stage during acquisition
• Smearing the powder with a glass slide to obtain a flat surface
• Using the largest possible divergence slit to boost intensity

Correct Answer: Back-loading the sample holder and spinning the stage during acquisition

Q9. In quantitative phase analysis by Rietveld refinement, which refined parameter primarily relates to the weight fraction of each crystalline phase?

• Zero shift
• Scale factor
• Background polynomial coefficients
• Peak FWHM (U, V, W parameters)

Correct Answer: Scale factor

Q10. Which observation most strongly indicates a polymorphic transformation after drying a crystalline API?

• Uniform shift of all peaks to higher 2θ without changes in relative intensities
• Peak broadening with no new peaks
• Replacement of the original reflections by a different set of peaks at different 2θ values
• Decrease in overall intensity but identical peak positions

Correct Answer: Replacement of the original reflections by a different set of peaks at different 2θ values

Q11. Grazing-incidence XRD (GIXRD) is most appropriate for which application in pharma materials analysis?

• Measuring bulk crystallinity of millimeter-thick tablets
• Characterizing crystalline coatings or surface phases on amorphous substrates
• Determining atomic coordinates of single crystals
• Eliminating preferred orientation in pressed pellets

Correct Answer: Characterizing crystalline coatings or surface phases on amorphous substrates

Q12. A formulation contains Fe-bearing excipients that fluoresce under Cu Kα, raising background. What is the most effective mitigation?

• Use Co Kα radiation to avoid Fe fluorescence
• Use larger divergence slits to overwhelm the fluorescence
• Reduce counting time to minimize background
• Raise the tube current to saturate the detector

Correct Answer: Use Co Kα radiation to avoid Fe fluorescence

Q13. What is the principal effect of unresolved Kα1/Kα2 doublets on powder diffraction peaks?

• Symmetric narrowing of peaks at all angles
• Asymmetric peak broadening and slight splitting, more evident at higher angles
• Complete suppression of low-angle peaks
• Shift of peak positions to lower 2θ uniformly

Correct Answer: Asymmetric peak broadening and slight splitting, more evident at higher angles

Q14. Why is an internal standard such as NIST SRM silicon added to some XRPD measurements?

• To increase fluorescence background for better statistics
• To calibrate the 2θ scale (zero/displacement) and instrument profile for accurate lattice parameters
• To enforce amorphization of the sample under study
• To reduce the need for sample spinning

Correct Answer: To calibrate the 2θ scale (zero/displacement) and instrument profile for accurate lattice parameters

Q15. Which statement correctly distinguishes size and microstrain broadening in XRPD?

• Size broadening increases with tan θ, strain broadening with 1/cos θ
• Both size and strain broadening increase with 1/cos θ
• Microstrain broadening scales with tan θ, while size broadening scales with 1/cos θ
• Neither depends on diffraction angle

Correct Answer: Microstrain broadening scales with tan θ, while size broadening scales with 1/cos θ

Q16. What is a key advantage of the Debye–Scherrer (capillary transmission) method for organic pharmaceuticals?

• It requires large flat pellets for optimal focusing
• It minimizes preferred orientation and allows sealed measurements for moisture-sensitive samples
• It eliminates the need for wavelength selection optics
• It prevents fluorescence in all samples

Correct Answer: It minimizes preferred orientation and allows sealed measurements for moisture-sensitive samples

Q17. In reciprocal space terms, when does diffraction occur according to the Ewald sphere construction?

• When any reciprocal lattice point lies inside the Ewald sphere
• When a reciprocal lattice point lies on the surface of the Ewald sphere
• Only when the origin of reciprocal space lies on the Ewald sphere
• When the Ewald sphere shrinks to zero radius

Correct Answer: When a reciprocal lattice point lies on the surface of the Ewald sphere

Q18. For Rietveld-quality data, why choose a small step size and sufficient counting time?

• To intentionally broaden peaks for easier fitting
• To resolve peak shapes and improve counting statistics, stabilizing refinements
• To reduce the number of observed reflections
• To eliminate the need for background modeling

Correct Answer: To resolve peak shapes and improve counting statistics, stabilizing refinements

Q19. Which XRPD approach is most appropriate to quantify amorphous content in a partially crystalline pharmaceutical?

• Differential scanning calorimetry alone
• Internal standard method with Rietveld/peak-modeling to compare crystalline peak intensities vs a known standard
• Optical microscopy of particle shapes
• FTIR peak height ratios

Correct Answer: Internal standard method with Rietveld/peak-modeling to compare crystalline peak intensities vs a known standard

Q20. Which practice best ensures radiation safety during routine powder XRD measurements?

• Operating with enclosure doors open for easier alignment
• Defeating interlocks to speed up measurements
• Using an interlocked enclosure and performing alignments with beam-off procedures
• Observing the primary beam visually to confirm alignment

Correct Answer: Using an interlocked enclosure and performing alignments with beam-off procedures

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