Name: magnetic field and nuclear precession
Uploaded: 2024-04-04T10:51:40.000Z
Duration: 1 min 11 s
Channel: JoVE

지구의 자전축은 세차운동(precession)이라고 불리는 현상으로 태양과 달의 중력 때문에 일정 기간 동안 흔들리고 변합니다.
유사하게, 회전하는 핵의 자기 모멘트 μ는 z축을 따라 지시된 적용된 자기장 B0로 인해 세차운동합니다.
여기서, 세차운동은 원뿔을 설명하기 위해 B0 필드 주위에서 회전하는 핵의 선회에 해당합니다.
자기장에 대한 자기 모멘트 벡터의 세차운동을 Larmor 세차라고 합니다. 세차 운동 또는 Larmor 주파수라고 하는 세차운동의 각도 주파수 ω는 B0에 정비례합니다.
자기장 비율 γ는 ω와 B0 사이의 비례 상수를 나타내며, 각 핵에 대해 고정되어 있습니다.
ω가 NMR 기기의 작동 주파수 ν로 표현되는 경우 항을 재배열하고 방정식의 양쪽에 플랑크 상수를 곱하면 ω와 ΔE 사이의 관계가 생성됩니다.

원자핵: 라머세차운동 진동수

Atomic Nuclei: Larmor Precession Frequency

지구의 중력장은 회전하는 질량(예: 팽이)의 각운동량에 수직인 '비틀림 힘'을 생성하며, 이로 인해 질량이 중력장 축 주위로 '흔들'게 됩니다. 이 현상을 세차운동이라고 합니다. 마찬가지로, 회전하는 핵의 자기 모멘트(μ)는 z축을 따라 향하는 외부 자기장으로 인해 세차 운동합니다. 자기장을 중심으로 한 자기모멘트 벡터의 세차운동을 라머세차운동이라 하고, 세차운동의 각주파수(Ω)를 세차 또는 라모주파수라 부르는데, 이는 인가된 자기장(B0)에 정비례합니다. 비례상수는 자이로자기비(γ)로, 각 핵마다 고정되어 있습니다. 이는 각 핵이 전하와 질량으로 인해 각운동량에 대한 자기 모멘트의 고유한 비율을 갖기 때문입니다. 수소 핵(양성자)의 경우 γ 값은 2.675 ×108 T−1 s−1.입니다. NMR 기기의 작동 주파수(ν)로 Ω를 표현하고, 항을 재배열하고, 방정식의 양쪽에 플랑크 상수를 곱하면 라모르 주파수와 스핀 상태 간의 에너지 차이(ΔE) 사이의 관계가 생성됩니다.

지구의 중력장은 회전하는 질량(예: 회전하는 팽이)의 각운동량에 수직인 '비틀림력'을 생성합니다.

atomic-nuclei-larmor-precession-frequency

Education

교육

JoVE Core

Analytical Chemistry

분석 화학

Unit 1

제1단원

Principles of Nuclear Magnetic Resonance

핵자기공명 원리

KEY TERMS AND CONCEPTS

주요 용어 및 개념

magnetic field and nuclear precession

Magnetic field strength controls nuclear precession in NMR. A spinning nucleus has a magnetic moment, and that moment turns around an external magnetic field directed along the z-axis. This motion is called Larmor precession, and its angular frequency is the Larmor frequency.

The Larmor frequency is directly proportional to the applied magnetic field, B0. The proportionality constant is the gyromagnetic ratio, gamma. This value is fixed for each nucleus because every nucleus has its own ratio of magnetic moment to angular momentum, which depends on its charge and mass.

A hydrogen nucleus, or proton, has a gyromagnetic ratio of 2.675 × 10^8 T−1 s−1. When omega is written in terms of the operating frequency, nu, of the NMR instrument, the equation can be rearranged. Multiplying both sides by Planck's constant gives the link between Larmor frequency and the energy gap, Delta E, between the spin states.

Magnetic Field and Nuclear Precession

nuclear magnetic resonance (nmr): overview

NMR Spectra and MRI Imaging

Nuclear magnetic resonance, or NMR, is a phenomenon that certain nuclei can show when they absorb radio frequency energy under the right conditions. Scientists use it in molecular spectroscopy and in medical imaging. In both cases, the sample or the person being studied is placed in a magnetic field and exposed to radio frequency energy. In NMR spectroscopy, the result is a spectrum. This spectrum plots the absorption frequencies of the sample against peak intensity. The pattern gives detailed...

atomic nuclei: nuclear spin

Nuclear Spin and NMR-Active Nuclei

Atomic nuclei have nuclear spin, which comes from the spins of their protons and neutrons. These particle spins are intrinsic angular momentum, and each electron, proton, and neutron has a spin value of 1/2. In nuclei, proton spins pair with other protons, and neutron spins pair with other neutrons. They do not pair with each other, so the final nuclear spin depends on which nucleons are left unpaired. Even numbers of protons do not add to the nuclear spin, and even numbers of neutrons do not...

atomic nuclei: nuclear magnetic moment

Nuclear Spin States and Magnetic Alignment

Atomic nuclei can act like tiny magnets when they have a nonzero spin. Because they are positively charged and rotating, they generate a magnetic field and a magnetic moment. In the absence of an external magnetic field, this magnetic moment points in random directions. When an external magnetic field, B0, is applied, the nuclear magnetic moments can line up with the field or against it. These two directions create 2I + 1 orientations. A hydrogen nucleus is a proton, and it has spin 1/2, so it...

atomic nuclei: nuclear spin state overview

atomic-nuclei-nuclear-spin-state-overview

Zeeman Splitting in Nuclear Spin States

NMR-active nuclei have spin states that describe the orientation of their nuclear magnetic moments. Without a magnetic field, these moments point in random directions, and the spin states are degenerate, meaning they have the same energy. When an external magnetic field is applied, the nucleus can only take on 2I + 1 orientations, where I is the nuclear spin. A proton with spin 1/2 has two possible orientations. A quadrupolar nucleus with spin 1 has three possible orientations. The...

atomic nuclei: nuclear spin state population distribution

atomic-nuclei-nuclear-spin-state-population-distribution

Nuclear Spin Populations and NMR Signal

Nuclear spin populations help explain why NMR signals appear. In a magnetic field, nuclei can occupy a lower energy spin-up state or a higher energy spin-down state. Near absolute zero, most nuclei stay in the lower energy state. As temperature rises, thermal collisions spread the spins more evenly between the two states. The balance between the spin −1/2 and spin +1/2 populations is described by the Boltzmann distribution equation. In this equation, ΔE is the energy difference, k is the...

atomic nuclei: larmor precession frequency

Magnetic field strength controls nuclear precession in NMR. A spinning nucleus has a magnetic moment, and that moment turns around an external magnetic field directed along the z-axis. This motion is called Larmor precession, and its angular frequency is the Larmor frequency. The Larmor frequency is directly proportional to the applied magnetic field, B0. The proportionality constant is the gyromagnetic ratio, gamma. This value is fixed for each nucleus because every nucleus has its own ratio...

atomic nuclei: magnetic resonance

Nuclear Spins and Resonance in a Magnetic Field

Nuclear spins can line up in a magnetic field and create nuclear magnetic resonance. In the lower energy state, slightly more spins are aligned than in the higher energy state. That small difference gives the nuclei a net magnetization along the z axis.

atomic nuclei: nuclear relaxation processes

atomic-nuclei-nuclear-relaxation-processes

Nuclear Spin Alignment and Relaxation

Nuclear spin alignment and relaxation describe how nuclear spins respond to a magnetic field and then return to equilibrium. Without an external magnetic field, nuclear spin states are degenerate, meaning they have the same energy, and the spins are randomly oriented. When a magnetic field is applied, the spins begin to precess, or wobble, and orient themselves either along the field in a lower energy state or against it in a higher energy state. At equilibrium, a slight excess of spins...

atomic nuclei: types of nuclear relaxation

atomic-nuclei-types-of-nuclear-relaxation

NMR Relaxation Paths in Atomic Nuclei

Nuclear relaxation in atomic nuclei helps restore the balance between energy levels in NMR systems. It occurs through two main paths: spin-lattice relaxation and spin-spin relaxation. Both are first-order exponential decay processes. Spin-lattice relaxation is also called longitudinal relaxation. In this process, excited spins give energy to the surrounding lattice as they move back to the lower energy level. Magnetic dipolar interactions are an important part of this mechanism. A common...

nmr spectrometers: overview

How NMR Spectrometers Record Signals

NMR spectrometers record signals from samples that contain NMR-active nuclei. The system uses a strong magnet, a radiofrequency transmitter, and a detector connected to a computer console. These parts work together to measure and display the spectrum of the sample. Early NMR instruments were continuous-wave spectrometers. In a frequency-sweep method, the magnetic field stays fixed while the rf signal is swept. In a field-sweep method, the radiofrequency signal stays fixed while the magnetic...

nmr spectrometers: radiofrequency pulses and pulse sequences

nmr-spectrometers-radiofrequency-pulses-and-pulse-sequences

NMR Pulse Angles and Signal Collection

NMR pulse angles and signal collection explain how radiofrequency energy starts a measurement. A pulse is a short burst of radio waves spread across a range of frequencies. It excites the nuclei in the sample at the same time. When a radiofrequency pulse is applied along the x-axis, nuclei absorb energy that matches their Larmor frequencies and reach resonance. The net magnetization vector moves away from the z-axis and toward the transverse plane. This rotation angle is called the flip angle.

nmr spectrometers: resolution and error correction

nmr-spectrometers-resolution-and-error-correction

NMR Peak Shape and Magnetic Field Shimming

NMR peak shape depends on the signal created after magnetic nuclei resonate and relax. The detected free induction decay is approximately exponential. When that decay is Fourier transformed, it becomes a Lorentzian peak in the frequency domain. A Lorentzian peak in an NMR spectrum is described by its amplitude, full width at half maximum, and position. Its width is governed by the spin-spin relaxation time alone. In real experiments, the sample and probe can make the magnetic field...

diamagnetic shielding of nuclei: local diamagnetic current

diamagnetic-shielding-of-nuclei-local-diamagnetic-current

How Electron Density Shields Nuclei in NMR

Electron density around a nucleus affects how strongly it is shielded in NMR spectroscopy. When an applied magnetic field acts on a molecule, the electrons begin to circulate. This creates a local diamagnetic current within the molecule. The circulating sigma-bonding electrons produce a local magnetic field, B local, that opposes the applied field, B0. The nucleus then feels an effective magnetic field, which is the difference between the applied field and the local field. This effect is...

key terms and concepts

See how an external magnetic field makes a nucleus precess, how Larmor frequency depends on B0, and why gamma matters for NMR spin states.

Magnetic Field and Nuclear Precession | JoVE K12

analytical chemistry

JoVE Core Analytical Chemistry simplifies complex chemical principles by breaking them down into clear, engaging animations, making topics from SI Units to NMR spectroscopy more accessible and straightforward. Additionally, the scientist-in-action videos highlight the application of these concepts in real-world research conducted in laboratories globally.

Magnetic Field and Nuclear Precession

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