Final answer:
The transition with the largest energy change is from n=2 to n=1, as this transition involves the largest change in the principal quantum number, reflecting the greatest difference in energy levels.
Step-by-step explanation:
Considering only the magnitude of the energy change during transitions in an atom, transitions involving larger changes in the principal quantum number (“n”) are associated with larger energy changes. According to the formula for the energy levels of the electron in a hydrogen atom, the energy is proportional to 1/n². Therefore, the greater the difference in the inverse squares of the initial and final quantum numbers, the greater the energy change of the transition.
The transition from n=2 to n=1 will have the largest change in energy since it involves the largest difference in the inverse squares (1/1² - 1/2² as opposed to, for example, 1/2² - 1/3² for the n=3 to n=2 transition). This can also be seen through the realization that energy levels are closer together at higher principal quantum numbers, indicating that transitions to and from the ground state (n=1) involve the most energy change. As per the Bohr model of the hydrogen atom, the described energy released is largest for the transition from the second excited state (n=3) directly to the ground state (n=1), as compared to step-by-step transitions like n=3 to n=2 followed by n=2 to n=1.