Magnetic Resonance Overview and Principles

This set of vocabulary flashcards covers the fundamental principles of nuclear magnetic resonance (NMR), including spin quantum numbers, angular momentum, magnetic dipoles, and factors affecting technique sensitivity.

Spin quantum number ($I$)

A positive integer or half-integer ($0, 1/2, 1, 3/2 ext{ etc.}$) that determines the size of the angular momentum vector for a nucleus.

Angular momentum vector ($\mathbf{I}$)

A vector used to describe nuclear spin, where the size of the vector measures the speed of rotation and its direction specifies the axis of rotation.

Magnetic dipole ($\mathbf{\mu}$)

The magnetic field associated with a nuclear spin, related to the angular momentum vector by the equation $\mathbf{\mu} = \gamma \mathbf{I}$.

Magnetogyric ratio ($\gamma$)

A nucleus-specific constant that relates the nuclear magnetic dipole to its angular momentum vector.

Quantisation axis ($z$)

The axis relative to which nuclear spin states are defined; the perpendicular ($xy$) components are undefined, causing the vector to lie on a cone for a given $m_I$ state.

NMR selection rule

The rule stating that an oscillating magnetic field causes transitions only between adjacent $m_I$ states, where $\Delta m_I = \pm 1$.

NMR frequency condition

The expression derived from the energy of transitions, given as $\nu = \frac{|\gamma| B}{2\pi}$, where absorption occurs when the photon energy matches the energy gap.

Boltzmann distribution

The distribution describing the number of molecules ($N_i$) in a given energy state at thermal equilibrium, determined by the ratio of energy gaps ($\Delta E$) to thermal energy ($k_B T$).

Polarisation ($P$)

The net population difference across transitions; in NMR, this value is approximately $3 \times 10^{-5}$ at Boltzmann equilibrium, leading to low sensitivity.

Hyperpolarisation

Techniques used to significantly increase polarisation ($P$) by transferring it from other sources, such as electron spins, to improve NMR sensitivity.

Quadrupolar nuclei

Nuclei with a spin quantum number I > 1/2, which often present challenges in NMR because their spectral lines can be extremely broad.

Receptivity

The overall sensitivity of a specific nucleus for NMR detection, which depends on its magnetogyric ratio ($\gamma$) and its natural abundance.