Relaxation processes in NMR MCQs With Answer

Introduction: Relaxation processes in NMR are central to understanding how nuclear spins return to equilibrium after perturbation, and they directly influence signal intensities, line shapes, and contrast in spectroscopy and imaging. For M. Pharm students, mastering relaxation mechanisms such as spin–lattice (T1), spin–spin (T2), dipole–dipole interactions, chemical shift anisotropy (CSA), and paramagnetic effects is essential for interpreting NMR data of drugs, metabolites and formulations. This blog presents focused multiple-choice questions with answers to deepen your grasp of theoretical models (BPP, Redfield), experimental measurement methods (inversion recovery, CPMG), spectral density functions, and how molecular motion and environment control relaxation behavior.

Q1. Which statement correctly defines the spin–lattice (T1) and spin–spin (T2) relaxation times in NMR?

• Spin–lattice (T1) is the time constant for loss of phase coherence in the transverse plane; spin–spin (T2) is the time for recovery of longitudinal magnetization.
• Spin–lattice (T1) refers to recovery of longitudinal magnetization to thermal equilibrium; spin–spin (T2) is the time constant for decay of transverse magnetization (dephasing).
• T1 and T2 are identical for all nuclei in all samples and correspond to the same physical process.
• T1 describes cross-relaxation between different spins only; T2 describes relaxation due to chemical exchange only.

Correct Answer: Spin–lattice (T1) refers to recovery of longitudinal magnetization to thermal equilibrium; spin–spin (T2) is the time constant for decay of transverse magnetization (dephasing).

Q2. For small organic molecules in fast isotropic solution, which relaxation mechanism most often dominates proton T1 and T2 relaxation?

• Chemical shift anisotropy (CSA)
• Dipole–dipole (dipolar) interactions between nuclei
• Scalar (J) coupling mediated relaxation
• Electric quadrupolar relaxation

Correct Answer: Dipole–dipole (dipolar) interactions between nuclei

Q3. According to Bloembergen–Purcell–Pound (BPP) theory, the T1 relaxation time reaches a minimum when which condition on the rotational correlation time τc and Larmor angular frequency ω0 is met?

• ω0 τc ≪ 1 (extreme narrowing)
• ω0 τc ≈ 1
• ω0 τc ≫ 1 (very slow motion)
• τc is independent of ω0 for the T1 minimum

Correct Answer: ω0 τc ≈ 1

Q4. For isotropic tumbling with a single correlation time τc, which form of the spectral density function J(ω) is used in simple relaxation models?

• J(ω) = τc / (1 + ω^2 τc^2)
• J(ω) = 1 / (1 + ω τc)
• J(ω) = ω^2 τc
• J(ω) = e^{-ω τc}

Correct Answer: J(ω) = τc / (1 + ω^2 τc^2)

Q5. Which pulse sequence is the standard method to measure T1 relaxation times experimentally?

• Inversion recovery sequence (180° – τ – 90°)
• Single spin echo (90° – τ – 180°)
• Hahn echo with multiple refocusing pulses
• NOESY (nuclear Overhauser enhancement spectroscopy)

Correct Answer: Inversion recovery sequence (180° – τ – 90°)

Q6. Which NMR sequence is typically used to measure T2 (transverse) relaxation while compensating for magnetic field inhomogeneity?

• Inversion recovery
• CPMG (Carr–Purcell–Meiboom–Gill) or spin-echo train
• Saturation recovery
• DEPT (Distortionless Enhancement by Polarization Transfer)

Correct Answer: CPMG (Carr–Purcell–Meiboom–Gill) or spin-echo train

Q7. Paramagnetic relaxation agents (e.g., Gd3+ complexes) added to a solution have what effect on observed proton relaxation times?

• They lengthen both T1 and T2 dramatically.
• They shorten both T1 and T2, often producing a larger proportional decrease in T1.
• They affect only T2 and leave T1 unchanged.
• They convert spin–1/2 nuclei into quadrupolar nuclei, eliminating NMR signals.

Correct Answer: They shorten both T1 and T2, often producing a larger proportional decrease in T1.

Q8. The heteronuclear NOE (e.g., 1H→13C) observed for small, rapidly tumbling molecules at high field typically has what sign and why?

• Negative enhancement, because cross-relaxation is dominated by slow motions.
• Positive enhancement, because dipolar cross-relaxation yields positive NOE in the extreme narrowing (fast tumbling) limit.
• Zero enhancement for all small molecules due to scalar coupling cancellation.
• Alternating positive and negative enhancements depending on the phase of the RF pulses only.

Correct Answer: Positive enhancement, because dipolar cross-relaxation yields positive NOE in the extreme narrowing (fast tumbling) limit.

Q9. How does relaxation driven by chemical shift anisotropy (CSA) scale with the external magnetic field strength B0 (or Larmor frequency ω0)?

• CSA-driven relaxation is independent of B0.
• CSA-driven relaxation scales approximately with ω0^0.5 (square root).
• CSA-driven relaxation scales approximately with ω0^2 (or B0^2).
• CSA-driven relaxation decreases with increasing B0.

Correct Answer: CSA-driven relaxation scales approximately with ω0^2 (or B0^2).

Q10. Which type of interaction does NOT contribute to relaxation for a nucleus that is spin-1/2 in a non-viscous isotropic liquid?

• Dipole–dipole interactions
• Chemical shift anisotropy (CSA)
• Scalar (J) coupling mediated relaxation
• Quadrupolar relaxation

Correct Answer: Quadrupolar relaxation

Q11. The Solomon equations are used in NMR to describe which phenomenon?

• The time evolution of magnetization under adiabatic pulses
• Cross-relaxation and NOE between two coupled spins including build-up and decay rates
• The chemical shift anisotropy tensor orientation averaging
• The effect of temperature on T1 linearly

Correct Answer: Cross-relaxation and NOE between two coupled spins including build-up and decay rates

Q12. What does T1ρ (T1rho) measure in NMR experiments?

• Spin–spin relaxation in the laboratory frame without RF fields
• Spin–lattice relaxation time measured in the rotating frame under continuous spin-lock RF irradiation
• The effective relaxation caused by field inhomogeneity only
• The relaxation time of quadrupolar nuclei only

Correct Answer: Spin–lattice relaxation time measured in the rotating frame under continuous spin-lock RF irradiation

Q13. For an ideal inversion recovery experiment (perfect 180° inversion), the longitudinal magnetization Mz(t) recovers according to which expression?

• Mz(t) = M0 (1 − e^{-t/T1})
• Mz(t) = M0 (1 − 2 e^{-t/T1})
• Mz(t) = M0 e^{-t/T2}
• Mz(t) = −M0 e^{-t/T1}

Correct Answer: Mz(t) = M0 (1 − 2 e^{-t/T1})

Q14. If a macromolecule becomes very large such that τc ≫ 1/ω0, what is the general trend for T1 relative to its minimum value?

• T1 decreases continuously as τc increases without bound.
• T1 approaches the same minimum value for all large τc.
• T1 increases again (becomes longer) as τc becomes much larger than 1/ω0.
• T1 becomes zero for very large τc.

Correct Answer: T1 increases again (becomes longer) as τc becomes much larger than 1/ω0.

Q15. Relaxation dispersion experiments (e.g., R2 dispersion or CPMG relaxation dispersion) are primarily used to probe dynamics on which timescale?

• Picoseconds (10^-12 s)
• Microseconds to milliseconds (10^-6–10^-3 s)
• Seconds to minutes (10^0–10^2 s)
• Nanoseconds only (10^-9 s)

Correct Answer: Microseconds to milliseconds (10^-6–10^-3 s)

Q16. Redfield theory, often used to derive relaxation rate expressions, is valid under which primary assumption?

• Strong coupling between spins with very long correlation times
• Weak system–bath coupling and Markovian (fast decay) correlation functions allowing perturbation theory
• Exactly equal T1 and T2 for all nuclei
• No molecular motion (static solids)

Correct Answer: Weak system–bath coupling and Markovian (fast decay) correlation functions allowing perturbation theory

Q17. How does the observed transverse relaxation rate R2* measured in a gradient- or field-inhomogeneous experiment compare with the intrinsic R2?

• R2* is always equal to R2.
• R2* is slower (smaller) than R2 because inhomogeneity reduces dephasing.
• R2* is larger (faster) than R2 because it includes contributions from B0 inhomogeneity and static dephasing.
• R2* applies only to heteronuclei and not to protons.

Correct Answer: R2* is larger (faster) than R2 because it includes contributions from B0 inhomogeneity and static dephasing.

Q18. The CPMG pulse train mitigates which relaxation-related artifact during measurement of transverse relaxation?

• Dipolar relaxation intrinsic to the molecule
• Signal loss due to chemical exchange only
• Dephasing caused by static magnetic field inhomogeneities (B0 variations)
• CSA-induced T1 shortening

Correct Answer: Dephasing caused by static magnetic field inhomogeneities (B0 variations)

Q19. Which of the following nuclei typically exhibits very fast relaxation because of quadrupolar interactions?

• 13C (spin-1/2)
• 1H (spin-1/2)
• 14N (spin-1), a quadrupolar nucleus
• 31P (spin-1/2)

Correct Answer: 14N (spin-1), a quadrupolar nucleus

Q20. If measured T1 and T2 values for a nucleus in solution are approximately equal (T1 ≈ T2), what does this imply about the molecular motion relative to the Larmor frequency?

• The motion is extremely slow: τc ≫ 1/ω0.
• The system is at the BPP T1 minimum: ω0 τc ≈ 1.
• The motion is in the extreme narrowing (fast) limit: τc ≪ 1/ω0.
• There is no molecular motion (rigid solid).

Correct Answer: The motion is in the extreme narrowing (fast) limit: τc ≪ 1/ω0.

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