Heisenberg Uncertainty principle relaxation

In the earlier treatment we reached the conclusion that resonance absorption occurs at the Larmor precessional frequency, a conclusion implying that the absorption line has infinitesimal width. Actually NMR absorption bands have finite widths for several reasons, one of which is spin-lattice relaxation. According to the Heisenberg uncertainty principle, which can be stated... 

Since the relaxation determines the lifetime, At, of a spin state, the Heisenberg Uncertainty Principle relates it to the uncertainty of the Zeeman eigenvalues, E and Ei, thereby allowing this phenomenon to affect the linewidth of EPR signals, as these depend inversely on T. ... 

While radiative relaxation can produce relatively narrow spectral lines (e.g. 0.0001 nm or less, depending on the source and line), the lines are not truly monochromatic. At the very least each spectral line exhibits a natural line width that is governed by the Heisenberg uncertainty principle... 

From the Heisenberg uncertainty principle, a magnetic nucleus will always give an NMR absorption band with finite width, even if it is not involved in a chemical exchange reaction. The minimum bandwidth can be related to the spin-lattice relaxation time, Tj, since the mean lifetime of the excited spin state cannot exceed Ti,... 

Relaxation of the momentum conservation rule is another important change when the crystallite size decreases to 1-2 nm. This can be understood in terms of Heisenberg s uncertainty principle Ap Ax > h. In a large single crystal of... 

Any atom being in an excited state, for instance after absorption of a photon, will undergo a relaxation process to a lower state within a finite time, even if there is no interaction with other atoms or molecules. Typical lifetimes r for undisturbed excited states are of the order of 10 to 10 s. After this the atom re-emits the photon and relaxes to the lower state, which is the ground state in the case of resonance transitions. According to Heisenberg s uncertainty principle AE At = h, the finite lifetime r causes an uncertainty of ... 

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