# What is the Dirac vector model in NMR?

##### 1 Answer

In **Nuclear Magnetic Resonance Spectroscopy**, the nucleus of every atom in the sample has a **magnetic moment**, giving it a nuclear spin.

The nuclear spin depends on the number of protons

- If the number of
#p^(+)# and#n^0# are EACH even, then the nuclear spin is#0# . - If the number of
#p^(+)# and#n^0# SUM to be odd, then the nuclear spin is#1/2, 3/2, . . . , n/2# where#n# is a positive odd integer. - If the number of
#p^(+)# and#n^0# are EACH odd, then the nuclear spin is#1,2,3,..., n# where#n# is a positive integer.

The magnetic moment interacts with an **applied magnetic field** **bulk magnetization** (the magnetization of the entire sample by the same magnetic field) is such that the ** net** magnetic field

*same direction*as the

**magnetic field**

*applied*The net magnetization can be represented as a single magnetization vector:

When a pulse of frequency *radio frequency* range is applied to the magnetic field, it tilts it away from the **Larmor precession**.

While the magnetization vector is tilted, **it rotates in the direction of the magnetic field**.

Using the right-hand-rule and noting that the precession frequency is ** negative**, the vector rotates

**(instead of counterclockwise like the right-hand rule would predict for a positive precession frequency).**

*clockwise*

The Larmor precession

#color(blue)(v_0 = -1/(2pi)gammaB_0)# where:

#nu_0# is thefrequencyof the applied pulse in#"Hz"# . A possible value for a Bruker NMR is#"300 MHz"# .#gamma# is thegyromagnetic ratioin#"1/T"cdot"s"# or#"1/G"cdot"s"# , depending on what units you want to use.#B_0# is theapplied magnetic fieldin either#"T"# (Tesla) or#"G"# (Gauss) for the magnetic field strength units;#"1 G = 10"^(-4) "T"# .

When you place a small **coil of wire** on the x-axis, it basically ** detects** the

*x component*of the Larmor precession, taking in a current induced by the magnetic field.

(This is like the induced current you can get when you send a magnetic field through a solenoid.)

If we suppose the magnitude of the vector is

This induced current is essentially *amplified* and *encoded* into an **NMR signal**.

That's about all you need to know, probably. You can read more about it here.

http://www-keeler.ch.cam.ac.uk/lectures/understanding/chapter_3.pdf