Bragg’s law MCQs With Answer

Bragg’s law MCQs With Answer equips M.Pharm students with targeted practice on the core diffraction principle that underpins powder X-ray diffraction (PXRD), single-crystal XRD, and small-angle scattering used in pharmaceutical analysis. From polymorph identification and excipient crystallinity assessment to lattice-spacing calculations for formulation science, Bragg’s law (nλ = 2d sinθ) connects measurable peak positions with the internal crystal structure. This quiz blends conceptual and numerical questions on variables (λ, d, θ, n), θ–2θ geometry, order of reflection, and cubic d–hkl relationships, with realistic pharmaceutical contexts. Use these MCQs to strengthen interpretation of diffractograms, understand how instrumental choices shift peaks, and avoid common pitfalls (e.g., using 2θ directly in Bragg’s equation). Precise thinking here translates into reliable solid-state characterization in the lab.

Q1. Which equation correctly states Bragg’s law for diffraction from crystal planes?

• nλ = 2d sinθ
• nλ = d sin2θ
• nλ = d/2 sinθ
• nλ = 2d/ sinθ

Correct Answer: nλ = 2d sinθ

Q2. In a θ–2θ powder diffractometer, what does θ represent in Bragg’s law?

• The angle between incident beam and detector
• Half of the diffractometer reading (2θ), i.e., the angle between the incident beam and lattice plane
• The full diffractometer angle (2θ)
• The crystal mosaic spread

Correct Answer: Half of the diffractometer reading (2θ), i.e., the angle between the incident beam and lattice plane

Q3. Using Cu Kα radiation (λ = 1.5406 Å), a peak appears at 2θ = 30° (first order). What is the interplanar spacing d?

• 1.24 Å
• 2.97 Å
• 3.54 Å
• 5.96 Å

Correct Answer: 2.97 Å

Q4. If the X-ray wavelength is increased while d and n are fixed, how do Bragg peak positions shift on a 2θ scale?

• To lower 2θ values
• To higher 2θ values
• No change in 2θ positions
• Peaks disappear entirely

Correct Answer: To higher 2θ values

Q5. Bragg’s law is satisfied when the path difference between waves reflected from adjacent planes equals:

• λ/2
• nλ
• 2nλ
• n/2 λ

Correct Answer: nλ

Q6. Which parameter does not appear in Bragg’s law and therefore does not affect peak positions directly?

• Wavelength (λ)
• Interplanar spacing (d)
• Bragg angle (θ)
• X-ray tube current (mA)

Correct Answer: X-ray tube current (mA)

Q7. For a crystal with d = 3.00 Å and λ = 1.5406 Å (first order), what is the expected peak position (2θ)?

• 14.9°
• 22.5°
• 29.8°
• 44.7°

Correct Answer: 29.8°

Q8. A powder diffractometer reports a peak at 2θ = 40°. What θ should be used in nλ = 2d sinθ?

• θ = 20°
• θ = 40°
• θ = 80°
• θ = 0°

Correct Answer: θ = 20°

Q9. For a cubic crystal (lattice parameter a = 5.0 Å), which plane has the largest d-spacing?

• (100)
• (110)
• (111)
• (210)

Correct Answer: (100)

Q10. Using Cu Kα (λ = 1.5406 Å), a first-order peak is at 2θ = 20°. What is d?

• 2.21 Å
• 3.08 Å
• 4.44 Å
• 8.88 Å

Correct Answer: 4.44 Å

Q11. Switching from Cu Kα (λ = 1.5406 Å) to Mo Kα (λ = 0.7093 Å) for the same sample causes Bragg peaks to:

• Shift to lower 2θ values
• Shift to higher 2θ values
• Remain at identical 2θ positions
• Disappear due to fluorescence

Correct Answer: Shift to lower 2θ values

Q12. If nλ > 2d for a given set of planes, what is observed experimentally?

• A very intense Bragg reflection
• No Bragg reflection because sinθ would exceed 1
• A reflection only at θ = 90°
• A reflection only at θ = 0°

Correct Answer: No Bragg reflection because sinθ would exceed 1

Q13. How does Bragg’s law support polymorph identification in pharmaceuticals?

• Different polymorphs have identical d-spacings, so peaks coincide
• Different polymorphs produce unique d-spacings, giving distinct 2θ fingerprints
• Bragg’s law only affects intensity, not peak positions
• Polymorphs can only be distinguished by NMR, not XRD

Correct Answer: Different polymorphs produce unique d-spacings, giving distinct 2θ fingerprints

Q14. In the small-angle limit (θ in radians), Bragg’s law approximates to which useful relation?

• d ≈ λ θ
• d ≈ λ/(2θ)
• d ≈ 2λ θ
• d ≈ θ/λ

Correct Answer: d ≈ λ/(2θ)

Q15. Which statement is true regarding Bragg’s law and diffraction peak characteristics?

• Bragg’s law dictates peak positions; intensities depend on structure factor and related terms
• Bragg’s law dictates both peak positions and intensities
• Bragg’s law dictates only peak intensities
• Bragg’s law is irrelevant to powder diffraction

Correct Answer: Bragg’s law dictates peak positions; intensities depend on structure factor and related terms

Q16. For a cubic crystal with a = 4.00 Å using Cu Kα (λ = 1.5406 Å), what is the 2θ for the (200) reflection (first order)?

• 22.7°
• 32.0°
• 45.3°
• 64.0°

Correct Answer: 45.3°

Q17. If the X-ray wavelength is halved while d and n remain fixed, how does θ change?

• θ doubles
• θ halves approximately (since sinθ ∝ λ)
• θ remains unchanged
• θ becomes zero

Correct Answer: θ halves approximately (since sinθ ∝ λ)

Q18. Preferred orientation in a powder sample primarily affects which aspect, given Bragg’s law?

• Peak positions (2θ)
• Peak intensities
• Wavelength of X-rays
• Interplanar spacing d

Correct Answer: Peak intensities

Q19. An organic API shows a lamellar spacing near 7.7 Å. Using Cu Kα (λ = 1.5406 Å), where will the first-order reflection approximately appear?

• 2θ ≈ 11.5°
• 2θ ≈ 23.0°
• 2θ ≈ 34.5°
• 2θ ≈ 46.0°

Correct Answer: 2θ ≈ 11.5°

Q20. For d = 2.50 Å and Cu Kα (λ = 1.5406 Å), what is the 2θ position of the second-order (n = 2) reflection?

• 2θ ≈ 30.0°
• 2θ ≈ 45.0°
• 2θ ≈ 60.0°
• 2θ ≈ 76.1°

Correct Answer: 2θ ≈ 76.1°

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