# 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.

## Answers and Replies

rj_duff
Ok - I'll answer my own question.

$$f=\frac{\gamma}{2\pi}B$$

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.