How much stronger are dipole transitions compared to quadrupole transitions?

Dipole transitions are generally much stronger than quadrupole transitions due to their differences in the allowed selection rules and the relative strengths of their corresponding matrix elements. The strength of a transition in quantum mechanics is often represented by the transition moment, which depends on the changes in the dipole moment for dipole transitions and in the quadrupole moment for quadrupole transitions.

Dipole transitions involve a change in the dipole moment of the molecule, which allows for a direct interaction with an electromagnetic field. This direct coupling means that dipole transitions are fundamentally more probable than quadrupole transitions. In contrast, quadrupole transitions, given their higher order nature, require changes in the quadrupole moment, resulting in a much smaller probability for these transitions to occur.

Quantitatively, it has been established that dipole transitions can be roughly estimated to be 100 times stronger than quadrupole transitions, which aligns with the value provided in the correct answer. This significant difference in strength is largely due to the inherent physical properties governing these two types of transitions, making the dipole interactions far more efficient in facilitating electronic transitions within atoms or molecules. Therefore, dipole transitions dominate in many spectroscopic applications and are much more relevant for understanding electronic spectra than