Electron cyclotron resonance - Motion of an electron in a magnetic field
Let us consider that a charged particle, namely an electron enters the magnetic field B of the Earth with a velocity v that is perpendicular to the magnetic field lines as shown in Figure 1. The magnetic field will exert a Lorenz force which will act as a centripetal. Under its influence the electron will run a cycle around the magnetic field lines, and it will actually continue running circles. In other words, it will gyrate or it will perform a cyclotronic motion.
Figure 1: Electron enters a magnetic field B with a velocity v that is perpendicular to B. It will perform a circular motion of radius R.
The natural frequency of rotation in such a magnetic field is called cyclotron frequency or gyrofrequency. It is given by the equation:
Figure 2: Illustration of the difference between the magnetic resonance frequency and the cyclotron resonance frequency.
Proton cyclotron resonance frequency and proton magnetic resonance frequency
What is the cyclotron frequency of the proton for 50μΤ?
It is 762,1 Hz. [ref.]
What is the proton magnetic resonance frequency for 50μΤ?
It is 2129 Hz or 2.1 KHz. This would be the frequency for an MRI at 50μΤ.
Ion cyclotron frequencies and magnetic resonance frequencies
What are the cyclotron frequencies for different ions?
What are the magnetic resonance frequencies for different ions?
Cl=209 Hz, K = 99 Hz, P = 863 Hz, Na= 563 Hz [ref.]