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Organic Chemistry · Structure Determination: Nuclear Magnetic Resonance Spectroscopy

Nuclear Magnetic Resonance Spectroscopy

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Constants: CODATA standard values; last updated 2026-08-16
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On this page 9 sections
  1. In 30 seconds
  2. Why this matters
  3. The college version
  4. Eli explains
  5. Worked example
  6. Key takeaway
  7. Check yourself
  8. Study tools
  9. Sources & references

In 30 seconds

Nuclear magnetic resonance (NMR) spectroscopy is the most information-rich tool in organic chemistry: it reveals the carbon skeleton and hydrogen environment of a molecule. The technique exploits spin, a property of certain nuclei: 1H and 13C behave like tiny bar magnets. In a strong magnetic field they point with or against the field, with slightly different energies, and radio-frequency (RF) photons whose energy matches that tiny gap flip them between orientations — resonance — at a frequency that depends on the electronic environment around each nucleus.

Because electrons shield nuclei to different degrees, chemically distinct hydrogens or carbons absorb at slightly different frequencies. The spectrum plots absorption intensity versus chemical shift (in ppm); each distinct H or C type gives its own signal. Counting, positioning, and splitting those signals maps a molecule's connectivity — which is why NMR is usually the final arbiter of structure.

Why this matters

NMR proves the identity and structure of synthetic and natural products and pharmaceuticals daily; no other method gives so much structural information so directly. The same physics powers magnetic resonance imaging (MRI), which images water protons in the body. In metabolomics, NMR profiles of blood or urine help diagnose disease. For students, 1H and 13C NMR problems — "how many signals, at what shifts, with what splitting?" — appear on virtually every organic exam.

The college version

Core Concepts

Which nuclei are NMR-active

A nucleus is NMR-active only if its spin quantum number I is not zero. The organic workhorses are 1H (I = 1/2, ≈ 99.98% abundant — essentially every hydrogen is visible) and 13C (I = 1/2, ≈ 1.1% — dilute, so 13C NMR needs signal averaging); 19F and 31P are also I = 1/2. Nuclei with even mass and even charge, like 12C and 16O, have I = 0 and are NMR-silent; I = 1/2 nuclei are preferred for their clean, narrow lines.

The resonance condition

A spin-1/2 nucleus in a magnetic field B0 has two allowed orientations, m = +1/2 (aligned with the field, lower energy) and m = -1/2 (against the field). The energy gap is:

ΔE = h γB02π

where γ is the gyromagnetic ratio (how strong a magnet the nucleus is). Absorption occurs when the RF photon energy equals the gap, hν= ΔE, giving the resonance (Larmor) frequency:

ν= γB02π

For 1H, γ/2π= 42.6 MHz/T; for 13C, 10.7 — about a quarter of the proton value. In a 1.41 T magnet, protons resonate near 60 MHz and 13C near 15 MHz; at 14.1 T, near 600 MHz. Instrument "field" is quoted by the proton frequency (a "400 MHz NMR" has B0 ≈ 9.4 T); the gap grows with field strength, so modern instruments use the strongest magnets.

Shielding and chemical shift

Electrons around a nucleus circulate in the applied field and generate a small induced field opposing B0 — they shield the nucleus, so the effective field is Beff = B0(1 - σ). A more shielded nucleus needs a slightly higher applied frequency to reach resonance and appears upfield (smaller shift); a deshielded nucleus — near electronegative atoms or in a π system — appears downfield (larger shift). Shifts are reported relative to tetramethylsilane (, Si(CH3)4, SMILES: C[Si](C)(C)C), assigned 0 ppm:

δ (ppm) = νsample - νTMSνinstrument × 106

Chemical shift δ is field-independent: the same proton shows the same δ at 60 and 600 MHz, even though its hertz offset is ten times larger on the bigger machine.

1H versus 13C NMR

  • 1H NMR (0–12 ppm): each chemically distinct set of hydrogens gives one signal; the integrated peak area is proportional to the number of hydrogens; spin–spin splitting (topics 6–8) reveals how many neighboring hydrogens each set has.
  • 13C NMR (0–220 ppm): each distinct carbon gives one signal; is not routinely used (areas are unreliable); the wide range distinguishes carbon types at a glance — carbonyl ~190–220, aromatic ~110–160, alkyne ~65–90, sp³ 0–90.

FT-NMR: pulsed instruments

Instead of sweeping frequency slowly, a modern spectrometer applies a short RF pulse containing all frequencies at once, then records the decaying signal (free induction decay, FID); a Fourier transform converts it to the familiar spectrum — the same math as FT-IR. This makes 13C NMR (1.1% abundant) practical via signal averaging.

Common Confusions

Do not confuseWithDifference
Chemical shift (ppm)Frequency offset (Hz)ppm is field-independent; Hz offset grows with B0. Convert with δ= (Δν/νinstrument) × 106
ShieldedDeshieldedShielded → upfield (smaller δ); deshielded (near O, N, π systems) → downfield (larger δ)
1H range13C range1H 0–12 ppm; 13C 0–220 ppm — never mix the scales
12C13C12C is NMR-silent (I = 0); only the 1.1% abundant 13C is observed
NMRMRISame physics; MRI images water protons; NMR analyzes molecular structure
Larger δ (downfield)Higher energy absorptionBoth true, but downfield = less shielded = higher RF frequency at fixed B0
IR photon energiesNMR photon energiesNMR RF photons (~10⁻²⁶ J) are far weaker than IR (~10⁻²⁰ J) — NMR is gentler
Eli, the EliExplains learning guide

Eli explains

The same idea, in plain words

Explain it like I’m 10

Certain atomic nuclei act like tiny compass needles, and a strong magnet lines them all up. A radio "push" of just the right strength flips them over, and each kind of atom needs a slightly different push depending on how its electron "armor" shields it. By measuring which pushes each hydrogen and carbon accepts, scientists draw the whole skeleton of the molecule.

Worked example

Example 1: Resonance frequencies of 1H and 13C at 1.41 T

Use the Larmor equation with γ/2π = 42.6 MHz/T (1H) and 10.7 MHz/T (13C):

ν(1H) = (42.6 MHz/T)(1.41 T) = 60.1 MHz

ν(13C) = (10.7 MHz/T)(1.41 T) = 15.1 MHz

At any field, 13C resonates at ~1/4 the proton frequency (at 14.1 T: ~600 vs ~150 MHz). Dimensional check: MHz/T × T = MHz. ✓

Example 2: Converting a hertz offset to a chemical shift

A proton absorbs 427 Hz downfield of TMS on a 60 MHz instrument. Find its chemical shift.

δ= νsample - νTMSνinstrument × 106 = 427 Hz60 × 106 Hz × 106 = 7.12 ppm

The Hz units cancel, leaving ppm. On a 400 MHz instrument, the same proton would absorb 7.12 × 10-6 × 400 × 106 = 2848 Hz — a much larger hertz offset, but the same 7.12 ppm. This is exactly why shifts are reported in ppm: the number is a property of the molecule, not the instrument.

Example 3: Why NMR signals are so weak — the Boltzmann population difference

At 60 MHz, the energy gap is:

ΔE = hν= (6.626 × 10-34 J·s)(60 × 106 s-1) = 3.98 × 10-26 J

The population ratio of the two spin states follows the Boltzmann distribution:

N+1/2N-1/2 = eΔE / kB T

At T = 300 K with kB = 1.381 × 10-23 J/K, ΔE/kB T = 3.98 × 10-26/((1.381 × 10-23)(300)) = 9.6 × 10-6.

The excess of spins in the lower state is only ~1 in 100,000, so absorption is extremely weak — stronger magnets (larger B0) help, and 13C's 4× smaller γ means 4× weaker signals, hence signal averaging. NMR photons are orders of magnitude below bond-breaking energies, making NMR non-destructive.

Key takeaways

  • NMR-active nuclei have spin I ≠ 0: 1H and 13C (I = 1/2) are the organic workhorses; 12C and 16O are silent.
  • Resonance frequency: ν= γB0/2π; 1H resonates ~4× higher than 13C (42.6 vs 10.7 MHz/T).
  • Shielding lowers the field at the nucleus; shielded → upfield (smaller δ), deshielded → downfield (larger δ).
  • Chemical shift is field-independent: δ= (νsample - νTMS) × 106 / νinstrument, referenced to TMS at 0 ppm.
  • 1H range 0–12 ppm with integration (area ∝ H count); 13C range 0–220 ppm, no routine integration.
  • 13C abundance is only ~1.1%, so 13C NMR relies on FT pulses and signal averaging.

Check yourself

4 review questions from the chapter. Try each one, then open the answer.

  1. Why are 12C and 16O invisible in NMR?

    Show answer

    They have I = 0 (even mass, even charge), so no nuclear magnetic moment and no resonance.

  2. A 1H signal appears 1420 Hz downfield of TMS on a 200 MHz instrument. What is its shift in ppm?

    Show answer

    δ= (1420 Hz / 200 × 106 Hz) × 106 = 7.10 ppm.

  3. Why does a deshielded proton appear downfield (larger δ)?

    Show answer

    Electron shielding reduces the field at the nucleus; a deshielded nucleus feels a larger effective field, so it resonates at a slightly higher applied frequency — a larger δ (downfield).

  4. Why is 13C NMR less sensitive than 1H NMR, and how is it compensated?

    Show answer

    13C is only ~1.1% abundant with a 4× smaller gyromagnetic ratio (weaker signal, smaller ΔE); FT-NMR pulses all frequencies at once and averages thousands of scans.

Keep learning

Ready to build on this? Continue to the next lesson.

Study tools & related lessonsKey vocabulary · Related

Key vocabulary

Nuclear spin (I)
Intrinsic nuclear angular momentum; I ≠ 0 for NMR
Shielding
Electrons reducing the field felt by a nucleus
Chemical shift (δ)
Field-independent signal position in ppm from TMS
TMS
Tetramethylsilane, Si(CH3)4
Integration
Peak area in 1H NMR, proportional to H count
FT-NMR
Pulsed NMR with Fourier transformation
FT–NMR
NMR using pulses plus Fourier transformation

Sources & references

  1. openstax.org — Organic Chemistry

This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.

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