Which one among the following transitions is associated with the largest change in energy in hydrogen atom?

In the Bohr model of the hydrogen atom, the energy of an electron at a specific level is given by E = -13.6/n² eV. The energy change during a transition is proportional to the difference between the squares of the reciprocals of the principal quantum numbers (1/n_final² - 1/n_initial²). Because the energy levels are quantized and follow an inverse-square relationship, the gap between levels decreases significantly as 'n' increases. The transition from n = 2 to n = 1 (Lyman series) involves a change of 1 - 1/4 = 0.75 units of the Rydberg constant. In contrast, transitions like n = 3 to n = 2 (Balmer series) involve only 1/4 - 1/9 ≈ 0.139 units. Thus, the jump to the ground state (n=1) from the first excited state (n=2) represents the largest energy difference among the given options.