8.2 Orbital magnetic dipole moment of the electron  (Page 2/8)

A hydrogen atom has a magnetic field, so we expect the hydrogen atom to interact with an external magnetic field—such as the push and pull between two bar magnets. From Force and Torque on a Current Loop , we know that when a current loop interacts with an external magnetic field $\overrightarrow{B}$ , it experiences a torque given by

where I is the current, $\overrightarrow{A}$ is the area of the loop, $\overrightarrow{\mathit{\text{μ}}}$ is the magnetic moment, and $\overrightarrow{B}$ is the external magnetic field. This torque acts to rotate the magnetic moment vector of the hydrogen atom to align with the external magnetic field. Because mechanical work is done by the external magnetic field on the hydrogen atom, we can talk about energy transformations in the atom. The potential energy of the hydrogen atom associated with this magnetic interaction is given by [link] :

If the magnetic moment is antiparallel to the external magnetic field, the potential energy is large, but if the magnetic moment is parallel to the field, the potential energy is small. Work done on the hydrogen atom to rotate the atom’s magnetic moment vector in the direction of the external magnetic field is therefore associated with a drop in potential energy. The energy of the system is conserved, however, because a drop in potential energy produces radiation (the emission of a photon). These energy transitions are quantized because the magnetic moment can point in only certain directions.

If the external magnetic field points in the positive z -direction, the potential energy associated with the orbital magnetic dipole moment is