Larmor Frequency of 57Fe the earth's ambient magnetic field

[rj_duff]

I would like to determine the Larmor frequency of 57Fe in the Earth's ambient magnetic field.

Properties \ Nuclide 57Fe
Nuclear Spin, I 1/2
Nuclear magnetic moment, µ +0.09044
Gyromagnetic Ratio (rad T-1 s-1) 0.8661 x 10 7
Quadrupole moment (m2) 0
Relative Sensitivity (1) 3.37 x 10 -5
Natural Abundance, % 2.1
Half-life,T1/2 stable
Absolute Sensitivity (2) 4.2 x 10 -3
Frequency (MHz) @ 2.3488 T 3.231

There is of course an North/South, East/West, and Vertical component which makeup the total magnetic field strength.

1. How would I calculate the Larmor frequency?

2. Do all the magnetic field components need to be accounted for?

I have found related pages on hyperphysics.com but do not have the background to follow everything presented, therefore, unable to determine the values to plug into the formulas.

Any help would be greatly appreciated.

 

[rj_duff]

Ok - I'll answer my own question.

[tex]f=\frac{\gamma}{2\pi}B[/tex]

Checking this formula against the above published frequency of 3.231MHz in a 2.3488T field:

(0.8661E7 / 2pi) * 2.3488 = 3.2377 MHz

The results are not in exact agreement - off by 6.68 KHz


Magnetic Field Values
Horizontal Intensity: 21,033.4nT
North Component: 20,753.7nT
East Component: 3418.7nT
Vertical Component: 48,890.4nT
Total Field: 53,222.9 nT

Calculating frequency based on the total field component:
(0.8661E7 / 2pi) * 53,222.9 = 73.365 Hz

Calculating frequency based on the vertical field component:
(0.8661E7 / 2pi) * 48,890.4nT = 67.393 Hz


From a practical standpoint, there is not that much variation in using the
vertical Vs total field component.

 

[astrokreng]

I understand your interest in determining the Larmor frequency of 57Fe in the Earth's ambient magnetic field. The Larmor frequency is defined as the frequency at which a nuclear spin precesses around the direction of an external magnetic field. In this case, we are interested in the Larmor frequency of 57Fe in the Earth's magnetic field, which is a combination of the Earth's main magnetic field and its smaller components (North/South, East/West, and Vertical).

To calculate the Larmor frequency, we can use the formula: ω = γB, where ω is the Larmor frequency, γ is the gyromagnetic ratio of 57Fe (0.8661 x 10^7 rad T^-1 s^-1), and B is the total magnetic field strength. In this case, we can assume that the Earth's magnetic field strength is 2.3488 T (tesla), as stated in the provided information.

Therefore, the Larmor frequency of 57Fe in the Earth's ambient magnetic field would be 2.034 x 10^8 Hz (hertz) or 203.4 MHz (megahertz). This means that the nuclear spin of 57Fe would precess at a frequency of 203.4 million times per second in the Earth's magnetic field.

To answer your second question, yes, all the magnetic field components need to be accounted for in order to accurately calculate the Larmor frequency. This is because the direction and strength of the magnetic field affect the precession of the nuclear spin.

I understand that the formulas and information on hyperphysics.com can be overwhelming, but I would suggest seeking guidance from a physics professor or a knowledgeable colleague to help you understand and apply the necessary values. Alternatively, you can also consult a physics textbook for further explanation and examples. I hope this helps and good luck with your research!