Quantum numbers in NMR MCQs With Answer

Introduction: Quantum numbers in NMR are fundamental to understanding how atomic nuclei interact with an external magnetic field and produce the spectra used in structure elucidation and drug analysis. This blog contains focused multiple-choice questions aimed at M. Pharm students studying Advanced Instrumental Analysis (MPA 201T). The quizzes connect quantum number concepts—nuclear spin (I), magnetic quantum number (mI), allowed transitions, selection rules, and practical consequences such as line multiplicity and relaxation—to NMR observables like resonance frequency, energy splitting and signal broadening. These questions emphasize conceptual depth and applied reasoning to help you master the quantum basis of NMR spectroscopy for pharmaceutical research and analysis.

Q1. What is the nuclear spin quantum number (I) for the 1H nucleus?

• 0
• 1/2
• 1
• 3/2

Correct Answer: 1/2

Q2. For a nucleus with spin quantum number I = 3/2, how many distinct magnetic sublevels (mI values) exist?

• 2
• 3
• 4
• 6

Correct Answer: 4

Q3. Which expression gives the number of allowed Zeeman energy levels for a nucleus with spin I?

• 2I
• 2I + 1
• I + 1
• I – 1

Correct Answer: 2I + 1

Q4. What are the allowed values of the magnetic quantum number mI for a nucleus with I = 1?

• mI = 0 only
• mI = −1/2, +1/2
• mI = −1, 0, +1
• mI = −3/2, −1/2, +1/2, +3/2

Correct Answer: mI = −1, 0, +1

Q5. In a magnetic field B0, the energy difference between adjacent mI levels for a spin-1/2 nucleus is proportional to which parameter?

• Planck’s constant only
• Gyromagnetic ratio and B0
• Temperature and concentration
• Electron shielding constant

Correct Answer: Gyromagnetic ratio and B0

Q6. The Larmor frequency ω0 of a nucleus is given by which relationship?

• ω0 = h / (kB·T)
• ω0 = γ · B0
• ω0 = 2π / T1
• ω0 = ΔE / (2I + 1)

Correct Answer: ω0 = γ · B0

Q7. Which selection rule applies to magnetic dipole transitions observed in conventional NMR?

• ΔmI = 0
• ΔmI = ±1
• ΔI = ±1
• ΔmI = ±2

Correct Answer: ΔmI = ±1

Q8. How many NMR transitions are possible between adjacent mI levels for a nucleus with I = 5/2?

• 2
• 3
• 5
• 6

Correct Answer: 5

Q9. Which nucleus is quadrupolar and often gives broadened NMR signals due to electric field gradients (I > 1/2)?

• 1H
• 13C
• 14N
• 31P

Correct Answer: 14N

Q10. The Boltzmann population difference between spin states in NMR is directly dependent on which of the following?

• Resonance line width
• Energy difference ΔE and temperature T
• Chemical shift only
• Spin–spin coupling constant J

Correct Answer: Energy difference ΔE and temperature T

Q11. For two identical spin-1/2 nuclei that are chemically equivalent, what is the total number of combined spin states?

• 2
• 3
• 4
• 6

Correct Answer: 4

Q12. Which quantum number is primarily used to describe the orientation of the nuclear spin relative to the external magnetic field?

• Principal quantum number n
• Orbital angular momentum l
• Magnetic quantum number mI
• Spin-orbit coupling constant

Correct Answer: Magnetic quantum number mI

Q13. The splitting of nuclear spin energy levels in an external B0 field is known as:

• Hyperfine coupling
• Zeeman effect
• Raman scattering
• Stark effect

Correct Answer: Zeeman effect

Q14. For an isotope with nuclear spin I = 0, what NMR signal is expected under normal magnetic resonance conditions?

• A sharp single resonance
• A multiplet of 2I + 1 lines
• No NMR signal from that nucleus
• Broad quadrupolar signal

Correct Answer: No NMR signal from that nucleus

Q15. Which parameter differentiates nuclei with identical I but different NMR resonance frequencies in the same B0 field?

• Spin multiplicity (2I + 1)
• Gyromagnetic ratio (γ)
• Number of mI levels
• Boltzmann constant

Correct Answer: Gyromagnetic ratio (γ)

Q16. In coupled spin systems, the term “spin quantum number” for an individual nucleus determines which practical NMR property?

• Chemical shift range in ppm
• Number of allowed magnetic transitions and multiplicity
• The sign of J coupling
• Solvent dependence of peaks

Correct Answer: Number of allowed magnetic transitions and multiplicity

Q17. Which statement about half-integer quadrupolar nuclei (e.g., I = 3/2) in high-resolution liquid-state NMR is correct?

• They always produce sharp multiplets similar to spin-1/2 nuclei.
• They are unaffected by electric field gradients in solution.
• They often show fast relaxation and broad signals due to quadrupolar interactions.
• They have no allowed magnetic transitions.

Correct Answer: They often show fast relaxation and broad signals due to quadrupolar interactions.

Q18. For a nucleus in a magnetic field, the quantum mechanical operator that corresponds to the z-component of spin uses which eigenvalues?

• mIħ where mI = −I, …, +I
• nħ where n = 1, 2, 3…
• l(l + 1)ħ where l = 0, 1, 2…
• Only ±1/2ħ for all nuclei

Correct Answer: mIħ where mI = −I, …, +I

Q19. Which of the following nuclei will produce the largest energy splitting ΔE in the same external field B0 (assuming natural γ values)?

• 13C
• 1H
• 15N
• 2H (deuterium)

Correct Answer: 1H

Q20. The resonance frequency difference between two isotopes of the same element in the same B0 is primarily due to:

• Different values of spin quantum number I
• Different gyromagnetic ratios (γ)
• Different Boltzmann populations
• Different chemical shift references

Correct Answer: Different gyromagnetic ratios (γ)

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