Q5(d). Chemical shift is independent of the spectrometer frequency

Introduction. The separation of a signal from TMS in hertz grows in proportion to the field (and so to the operating frequency). Dividing by the operating frequency gives the chemical shift δ, a field-independent number in parts per million:

δ (ppm) = (Δν (Hz))/(ν₀ (MHz))

1. At 60 MHz: δ = (120 Hz)/(60 MHz) = 2.00 ppm
2. δ is a ratio of a frequency difference to the operating frequency; both scale with B₀, so δ is the same on every instrument: at 100 MHz, δ = 2.00 ppm.
3. At 100 MHz: Δν = δ × ν₀ = 2.00 × 100 = 200 Hz

Figure: The signal stays at δ 2.00; its distance in Hz scales with ν₀.

1. Since ν = γ B₀(1-σ)/2π, both the signal–TMS separation and ν₀ are proportional to B₀; their ratio depends only on the shielding constant σ, a property of the nucleus in its molecule.
2. Coupling constants J (in Hz) do not change with the field; so at 100 MHz multiplets occupy a smaller δ range and overlap less: higher-field instruments give spectra closer to first order.

Conclusion. (i) δ = 2.00 ppm; (ii) δ = 2.00 ppm (independent of the instrument); (iii) Δν = 200 Hz downfield from TMS at 100 MHz.

Application. Reporting shifts in δ lets spectra recorded at 60, 300 or 600 MHz be compared directly; a 2.0 ppm signal is typical of CH₃CO⁻ or CH₃-C=C protons.