When do you use the Boltzmann Distribution in NMR?

Answer 1

You use the Boltzmann distribution to calculate the relative number of nuclei in each spin state.

In a magnetic field, the magnetic moments of the nuclei can align either antiparallel (higher energy) or parallel to the field (lower energy).

The energy separation #ΔE# between these states is relatively small, and the energy from thermal collisions is sufficient to place many nuclei into higher energy spin states.

For every spin state, the number of nuclei is described by the Boltzmann distribution.

#N_+/N_(-) = e^-((ΔE)/(kT))#
At room temperature, the number of spins in the lower energy level, #N_-#, slightly outnumbers the number in the upper level, #N_+#.

When operating at 298 K and 60 MHz,

#N_+/N_(-) = "1 000 000"/"1 000 009"#

Stated differently, there is a population excess of roughly 9 in 2 million molecules in the lower energy spin state.

Using a higher frequency (increasing #ΔE#) increases the population excess.
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Answer 2

The Boltzmann Distribution is used in NMR spectroscopy to describe the population distribution of nuclear spin states in a magnetic field at thermal equilibrium. This distribution helps in understanding the relative populations of different energy levels, which is crucial for interpreting NMR spectra.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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