(a) In many instances it is possible to approximate the NMR lineshape by using a Lorentzian function of the form

where I(ω) is the intensity as a function of the angular frequency ω=2πν, ω₀ is the resonance frequency, S₀ is a constant, and T₂ is the spin–spin relaxation time. Confirm that for this lineshape the width at half-height is 1/πT₂.

(b) Under certain circumstances, NMR lines are Gaussian functions of the frequency, given by

Confirm that for the Gaussian lineshape the width at half-height is equal to 2(ln 2)^1/2/T₂.

(c) Compare and contrast the shapes of Lorentzian and Gaussian lines by plotting two lines with the same values of S₀, T₂, and ω₀.

Transcribed Image Text:

ILorentzian (@)= So T₂ 1+T₂²(w-wo)²