Texas A&M University (TAMU) CHEM107 General Chemistry for Engineering Students Exam 2 Practice

The transition that corresponds to the longest wavelength is associated with the lowest energy photon. Wavelength and energy are inversely related through the equation \(E = \frac{hc}{\lambda}\), where \(E\) is the energy of the photon, \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength.

When energy decreases, the wavelength increases; thus, the lowest energy transition will yield the longest wavelength. This principle follows the fundamental relationship that as one property (wavelength) increases, the other property (energy) must decrease to maintain a constant value, as represented in the equation.

In the context of photon transitions, if a system undergoes a transition that involves the lowest energy level, the emitted or absorbed photon will have a longer wavelength compared to transitions involving higher energy levels. Therefore, the answer identifying the lowest energy transition as that which corresponds to the longest wavelength is fundamentally based on the principles of photon energy and wavelength relationship.