The correct answer is option 3, n = 3 to n = 2, because this transition involves the largest change in energy in a hydrogen atom.

In the hydrogen atom, the energy of an electron is quantized and depends on its energy level, which is represented by the principal quantum number (n). As the electron moves from a higher energy level to a lower energy level, it releases energy in the form of electromagnetic radiation.

The energy of an electron in a hydrogen atom is given by the equation E = -13.6/n^2 electron volts (eV), where n is the principal quantum number.

When an electron transitions from n = 3 to n = 2, there is a larger change in the principal quantum number compared to the other options provided. The energy change in this transition can be calculated using the equation ΔE = E(initial) - E(final) = -13.6/2^2 - (-13.6/3^2) = -3.4 + 1.511 = -1.889 eV.

Therefore, option 3, n = 3 to n = 2, is associated with the largest change in energy in a hydrogen atom.