<P> Following the pulse, the nuclei are, on average, excited to a certain angle vs. the spectrometer magnetic field . The extent of excitation can be controlled with the pulse width, typically ca . 3 - 8 μs for the optimal 90 ° pulse . The pulse width can be determined by plotting the (signed) intensity as a function of pulse width . It follows a sine curve, and accordingly, changes sign at pulse widths corresponding to 180 ° and 360 ° pulses . </P> <P> Decay times of the excitation, typically measured in seconds, depend on the effectiveness of relaxation, which is faster for lighter nuclei and in solids, and slower for heavier nuclei and in solutions, and they can be very long in gases . If the second excitation pulse is sent prematurely before the relaxation is complete, the average magnetization vector has not decayed to ground state, which affects the strength of the signal in an unpredictable manner . In practice, the peak areas are then not proportional to the stoichiometry; only the presence, but not the amount of functional groups is possible to discern . An inversion recovery experiment can be done to determine the relaxation time and thus the required delay between pulses . A 180 ° pulse, an adjustable delay, and a 90 ° pulse is transmitted . When the 90 ° pulse exactly cancels out the signal, the delay corresponds to the time needed for 90 ° of relaxation . Inversion recovery is worthwhile for quantitive C, 2D and other time - consuming experiments . </P> <P> A spinning charge generates a magnetic field that results in a magnetic moment proportional to the spin . In the presence of an external magnetic field, two spin states exist (for a spin 1 / 2 nucleus): one spin up and one spin down, where one aligns with the magnetic field and the other opposes it . The difference in energy (ΔE) between the two spin states increases as the strength of the field increases, but this difference is usually very small, leading to the requirement for strong NMR magnets (1 - 20 T for modern NMR instruments). Irradiation of the sample with energy corresponding to the exact spin state separation of a specific set of nuclei will cause excitation of those set of nuclei in the lower energy state to the higher energy state . </P> <P> For spin 1 / 2 nuclei, the energy difference between the two spin states at a given magnetic field strength is proportional to their magnetic moment . However, even if all protons have the same magnetic moments, they do not give resonant signals at the same frequency values . This difference arises from the differing electronic environments of the nucleus of interest . Upon application of an external magnetic field, these electrons move in response to the field and generate local magnetic fields that oppose the much stronger applied field . This local field thus "shields" the proton from the applied magnetic field, which must therefore be increased in order to achieve resonance (absorption of rf energy). Such increments are very small, usually in parts per million (ppm). For instance, the proton peak from an aldehyde is shifted ca . 10 ppm compared to a hydrocarbon peak, since as an electron - withdrawing group, the carbonyl deshields the proton by reducing the local electron density . The difference between 2.3487 T and 2.3488 T is therefore about 42 ppm . However a frequency scale is commonly used to designate the NMR signals, even though the spectrometer may operate by sweeping the magnetic field, and thus the 42 ppm is 4200 Hz for a 100 MHz reference frequency (rf). </P>

Discuss the importance of nmr analysis for organic molecules