Final answer:
The largest change in energy occurs during a transition from n = ∞ to n = 1, with n representing the vibrational quantum number. This is due to the quantization of energy levels and the increasing difference between them with higher quantum numbers.
Step-by-step explanation:
Considering only the magnitude, the transition associated with the largest change in energy is the transition from a very high vibrational quantum number to a low one, specifically from n = ∞ to n = 1. This corresponds to the largest possible change since the energy levels are quantized and the difference between them increases with the quantum number.
In the context of diatomic molecules, transitions involving changes in both vibrational (n) and rotational (j or I) quantum numbers determine the energy change associated with the absorption or emission of radiation. However, under the selection rules for electric dipole transitions, the change in rotational quantum number, ΔI, must be +1, with I being associated with the magnitude of orbital angular momentum.
This ensures transitions where rotational energy increases, such as j → j + 1. The absorption spectrum for these transitions can exhibit peaks with energies calculated by formulas such as ΔE1→1+1 = ℏw +2Eor, ℏw + 4Eor, ℏw+6Eor, and so forth, with w representing vibrational frequency and Eor rotational energy.