Hello friends welcome once again on our blog. In our last post we’ve discussed Pauli’s Exclusion Principle. In this post we are going to discuss Larmor Precession which is another important topic in Atomic Physics.
Note for Reader’s :- the bold letters (e.g. B ) represents vector B.
An electron moving around the nucleus of an atom is equivalent to a magnetic dipole.
Hence when an ayřtom is placed in external magnetic field, the electron orbit precessesabout the field direction as axis.The precession is called Larmor’s Precession.
Let vector B is the external magnetic field and L is the orbital angular momentum of the electron.
Let θ be the angle between L and B.
The orbital dipole moment μι of electron is given by :
The torque τ on electron produces a change dL in angular momentum L in a time dt. The change dL is perpendicular to L.
Hence the angular momentum L remains constant in magnitude but its direction changes.
Therefore L traces a cone around B such that the angle between them is constant. This is the precession of L and hence the electron orbit around B.
|Fig 1. Larmor Precession
If ω be the angular velocity of precession, then L precesses through an angle ωdt in time dt. From fig.1.
Since, angle = arc/radius
Thus, the angular velocity of Larmor’s precession is equal to product of the magnitude of magnetic field, and the ratio of magnetic moment to magnitude of angular momentum.
It is independent of orientation angle…….. lies between normal (L) and field direction (B)
Importance : This theorem is of considerable importance in atomic structure as it enables an easy calculations of energy levels in presence pf external magnetic field.
This is Larmor’s Precession. You can ask any question related to this post in comment section.