Question

Explain why we need/want a large magnetic field in NMR based on the following concepts:

a. kT and the Boltzmann distribution

b. the energy difference between the ground and excited states

c. the net magnetization of the sample

Answer 1

At room temp, the number of spins in the lower energy level (N+) is slightly greater than the number in the upper level (N-). The NMR signal depends on this difference in population. The greater the field B₀, the greater the population difference. so the signal will be good.

a) according ro the equation N_upper  /N_lower = e^-γBo/kT where γ is the gyromagnetic ratio, Ns is the number of spins, Bo is magnetic field strength, k is the Boltzmann constant, and T is absolute temperature. If  In other words, the upper and lower energy spin states are almost equally populated with only a very small excess in the lower energy state. Inorder to increase the difference, we need a large magnetic field in NMR.

Boltzmann distribution is about "When the nucleus is in a magnetic field, the initial populations of the energy levels are determined by thermodynamics", it means that the lower energy level will contain slightly more nuclei than the higher level. It is possible to excite these nuclei into the higher level with electromagnetic radiation. The frequency of radiation needed is determined by the difference in energy between the energy levels.

from the equation .... if the magnetic field, B, is increased, so is DE. It also means that if a nucleus has a relatively large magnetogyric ratio, then deltaE is correspondingly large.

b) As we discussed earlier, if the energy difference is less, the difference in population will be less. So the NMR signal will not be prominent. To increase the  difference in population, we require to input energy in the form of magnetic field. SO if the magnetic field hight, the energy difference will be high. SO the signal will be clear.

c) The net field from all these little compasses summed together is equivalent to the net magnetization vector M. The maximum value of net magnetization at equilibrium along the direction of the main magnetic field (Bo) is denoted Mo. As we will show in later Q&A's, Mo determines the maximum amount of signal it is possible to generate from an NMR/MRI experiment. Mo  ≈ γ² h² Ns Bo / 4kT

So Mo is directly propotional to Bo.