Quantum numbers in NMR MCQs With Answer

Quantum numbers in NMR MCQs With Answer

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Quantum Numbers in NMR MCQs With Answer for M.Pharm Students

Nuclear Magnetic Resonance (NMR) relies on quantum mechanical properties of nuclei, especially the nuclear spin quantum number (I) and its magnetic projection (mI). Grasping these quantum numbers helps explain why some nuclei are NMR-active, how many Zeeman energy levels exist, which transitions are allowed, and why line widths differ across nuclei. This MCQ set focuses on I, mI, gyromagnetic ratio (γ), Larmor precession, selection rules (Δm = ±1), and consequences such as quadrupolar broadening and sensitivity trends. Tailored for Modern Pharmaceutical Analytical Techniques, these questions connect fundamental spin physics with practical spectral interpretation, supporting accurate structure elucidation, coupling analysis, and informed nucleus selection in pharmaceutical research.

Q1. In NMR, what does the nuclear spin quantum number (I) primarily determine?

  • The number of allowed magnetic sublevels (2I + 1) in a magnetic field
  • The exact chemical shift in ppm
  • The radiofrequency power needed for excitation
  • The solvent susceptibility

Correct Answer: The number of allowed magnetic sublevels (2I + 1) in a magnetic field

Q2. For a nucleus with I = 3/2, which set lists all allowed mI values?

  • -3/2, -1/2, +1/2, +3/2
  • -3/2, 0, +3/2
  • -1, 0, +1
  • -2, -1, 0, +1, +2

Correct Answer: -3/2, -1/2, +1/2, +3/2

Q3. What is the magnetic dipole selection rule for NMR transitions between Zeeman levels?

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

Correct Answer: ΔmI = ±1

Q4. The Larmor resonance frequency (ν₀) of a nucleus is given by which expression?

  • ν₀ = (γ/2π) B₀
  • ν₀ = γħB₀
  • ν₀ = γB₀²
  • ν₀ = (ħ/2π) B₀

Correct Answer: ν₀ = (γ/2π) B₀

Q5. For a spin-1/2 nucleus, the energy gap (ΔE) between the two Zeeman levels in a field B₀ is:

  • ΔE = γħB₀
  • ΔE = 2γħB₀
  • ΔE = γB₀/ħ
  • ΔE = ħ/γB₀

Correct Answer: ΔE = γħB₀

Q6. The nuclear spin quantum number (I) for ¹H (proton) is:

  • 1/2
  • 1
  • 3/2
  • 0

Correct Answer: 1/2

Q7. Which of the following nuclei are NMR-inactive due to I = 0?

  • ¹²C and ¹⁶O
  • ¹³C and ¹⁹F
  • ³¹P and ²H
  • ¹H and ¹⁵N

Correct Answer: ¹²C and ¹⁶O

Q8. Which rule correctly links nuclear composition with spin quantum number I?

  • Even Z and even N → I = 0
  • Odd mass number (A) → I is integer
  • Even Z and even N → I is half-integer
  • Odd Z and odd N always → I = 0

Correct Answer: Even Z and even N → I = 0

Q9. In a purely Zeeman-split system, a nucleus with I = 2 will show how many allowed transitions?

  • 4
  • 2
  • 3
  • 5

Correct Answer: 4

Q10. Deuterium (²H) has which spin quantum characteristics?

  • I = 1 with three mI levels
  • I = 1/2 with two mI levels
  • I = 3/2 with four mI levels
  • I = 0 with one mI level

Correct Answer: I = 1 with three mI levels

Q11. For nuclei with a negative gyromagnetic ratio (γ), which statement is correct?

  • The ordering of mI energy levels is reversed compared with a positive-γ nucleus at the same B₀
  • NMR transitions become forbidden (ΔmI = 0)
  • The number of Zeeman levels changes
  • The nucleus becomes NMR-inactive

Correct Answer: The ordering of mI energy levels is reversed compared with a positive-γ nucleus at the same B₀

Q12. The z-component of the nuclear magnetic moment is given by:

  • μz = γħmI
  • μz = ħmI/γ
  • μz = γħI
  • μz = γB₀mI

Correct Answer: μz = γħmI

Q13. The magnitude of the nuclear spin angular momentum is:

  • |I| = ħ√[I(I + 1)]
  • |I| = ħI
  • |I| = γħI
  • |I| = √(γB₀/ħ)

Correct Answer: |I| = ħ√[I(I + 1)]

Q14. Nuclei with I ≥ 1 possess an electric quadrupole moment. In solution NMR this mainly causes:

  • Rapid relaxation and line broadening
  • Large upfield chemical shifts
  • Complete suppression of Zeeman splitting
  • Higher natural abundance

Correct Answer: Rapid relaxation and line broadening

Q15. For coupling with n equivalent spins of spin I, the first-order multiplicity of a resonance is:

  • 2nI + 1
  • n + I
  • nI
  • 2I + 1

Correct Answer: 2nI + 1

Q16. Which set lists all allowed mI values for a spin-1 nucleus?

  • -1, 0, +1
  • -1/2, +1/2
  • -3/2, -1/2, +1/2, +3/2
  • 0 only

Correct Answer: -1, 0, +1

Q17. Considering nitrogen isotopes, which statement about line width and spin is most accurate?

  • ¹⁴N (I = 1) often gives broad lines due to quadrupolar relaxation; ¹⁵N (I = 1/2) gives sharper lines
  • ¹⁴N (I = 1) gives sharper lines than ¹⁵N
  • Both ¹⁴N and ¹⁵N are I = 0 and show no NMR signals
  • ¹⁴N and ¹⁵N have identical line widths in solution

Correct Answer: ¹⁴N (I = 1) often gives broad lines due to quadrupolar relaxation; ¹⁵N (I = 1/2) gives sharper lines

Q18. Why do nuclei with I = 0 not exhibit an NMR signal?

  • They lack Zeeman splitting because there is only mI = 0
  • They precess too fast to detect
  • They have zero mass number
  • They cannot be placed in a magnetic field

Correct Answer: They lack Zeeman splitting because there is only mI = 0

Q19. For a positive-γ, spin-1/2 nucleus in a magnetic field, which state is more populated at thermal equilibrium?

  • The mI = +1/2 state (aligned with B₀)
  • The mI = -1/2 state (opposed to B₀)
  • Both states are equally populated
  • The higher-energy state

Correct Answer: The mI = +1/2 state (aligned with B₀)

Q20. In the Zeeman interaction, the energy of a nuclear spin state depends linearly on which quantum number?

  • mI
  • I only
  • l (orbital angular momentum)
  • Principal quantum number n

Correct Answer: mI

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