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The angular frequency associated with a "spin flip", a resonant absorption or emission involving the spin quantum states is often written in the general form ω = g B where g is called the gyromagetic ratio (sometimes the magnetogyric ratio).
Who was Larmor and how did he discover his famous frequency? Sir Joseph Larmor was an Irish-born mathematical physicist whose career spanned from the late 19th to the early 20th Century. For many years he served as the Lucasian Professor of Mathematics at St. John's College, Cambridge.
This is the so-called Larmor frequency. Indeed, this identification is standard in mechanics. A vector v rotating with angular velocity ω satisfies the differential equation . dv = ω × v . (2.21) dt. You can convince yourself of this with the help of a simple picture (see Figure 1) . Also note
Jan 30, 2023 · Larmor Precession. Page ID. When placed in a magnetic field, charged particles will precess about the magnetic field. In NMR, the charged nucleus, will then exhibit precessional motion at a characteristic frequency known as the Larmor Frequency. The Larmor frequency is specific to each nucleus.
The Larmor frequency can be visualized classically in terms of the precession of the magnetic moment around the magnetic field, analogous to the precession of a spinning top around the gravity field. It can also be visualized quantum mechanically in terms of the quantum energy of transition between the two possible spin states for spin 1/2.
Transitions between the two states can be induced by absorption or emission of a photon of frequency n 0, such that (2.11) Expressing the frequency in angular terms gives the Larmor equation which underpins the whole of NMR (2.12) the characteristic frequency, w, being the Larmor frequency.
Aug 18, 2021 · So, the emitted photon has a frequency which is equal to the oscillation frequency of the system! We can also calculate the lifetime of the state, τ ∼ 1 / A {\displaystyle \tau \sim 1/A} : τ = 6 π ϵ 0 m c 3 n q 2 ω 2 . {\displaystyle \tau ={\frac {6\pi \epsilon _{0}mc^{3}}{nq^{2}\omega ^{2}}}.\,\!}
