Question

2. The Larmor Precession Frequency is the frequency at which a nucleus, whose magnetic moment is not aligned with an exterior B-field, precesses around the direction of the B-field. (a) Show that the Larmor precession frequency for a hydrogen atom in a 10 T mag- netic field is 4.26 x 108 Hz. (b) Does the Larmor precession frequency increase or decrease when the B-field is dropped to 5 T. (c) Does the Larmor precession frequency increase or decrease if it were 13C in a 10 T B-field instead.

Answer 1

Solution:

a) For an Atom having a Nucleus whose Magnetic Moment is not Aligned with an External Magnetic Field; the Larmor Precession Frequency can be calculated by using Equation:

Omega = Gamma × B, where;

Omega-Larmor Precession Frequency

Gamma-Gyromagnetic Ratio of Atom(Ratio of Magnetic Moment of an Atom to the Orbital Angular Momentum).

B-External Magnetic Field.

For 1H Atom the Gyromagnetic Ratio(Gamma) is 42.58MHz/Tesla

So if the 1H Atom is placed in a 10 T Magnetic Field,then;

Larmor Precession Frequency (Omega)=42.58MHz/T ×10 T

= 425.8 MHz = 4.26 ×108 Hz

b) As Larmor Precession Frequency is directly Proportional to the Magnetic Field Strength, if the B is decreased from 10T to 5T,then Omega decreases to Half.

i.e; Omega= Gamma × B

= 4.26×107 Hz × 5T = 2.13×108 Hz.

c) The Gyromagnetic Ratio is a specific value for every Atom.The Gamma of 13C Atom only about 1/4th of 1H Atom = 10.7MHz/T

So if the 1H Atom is replaced with 13C Atom in a Magnetic Field of 10T,then Omega decreases to 1/4th of Omega of 1H Atom.

Omega= 10.7MHz/T × 10T

= 107Hz = 1.07×108 Hz.

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