# NMR: What is the magnetic field of coalescence in a symmetrical two-site exchange?

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Question description

Question 1.

Consider an idealized symmetrical two-site exchange process, with kinetics described by the Arrhenius equation over a wide range in temperature. The pre-exponential constant is A = 1014 s-1 and the activation energy is Eact = 60 kJ mol-1. The exchange process causes a change in the 13C chemical shift at a certain molecular site to change by 30 ppm, while the 1H chemical shift at a different molecular site changes by 4 ppm. All the parameters are assumed to be temperature independent.

(i) At what magnetic field is the coalescence in the 13C line shapes observed if the sample temperature is T = 300 K? Hint: coalescence occurs at point where 𝑘 = (dA-dB)/2*sqrt2, where k is exchange rate and dA, dB are chemical shift in environment A and B.  (ii) At what magnetic field is the coalescence in the 1H line shapes observed if the sample temperature is T = 300 K?  (iii) At what temperature is the coalescence in the 1H line shapes observed if the proton Larmor frequency is ω0/2π = −300 MHz? (iv) Around which temperature does one expect the exchange process to become a mechanism for proton spin–lattice relaxation if the magnetic field is B0 = 14 T?

Please check upload. Question is from Spin Dynamics: Basics of NMR by M.H. Levitt, Exercise 19.1

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