Final answer:
The transition that produces the light of the lowest frequency in the hydrogen atom is from n = 4 to n = 5, as it has the smallest energy difference and therefore emits light at the lowest frequency.
Step-by-step explanation:
The electron transition that produces light of the lowest frequency in the hydrogen atom is the one with the smallest energy difference between the two involved energy levels. According to the Bohr model of the hydrogen atom, when an electron transitions from a higher energy level to a lower one, a photon is emitted with an energy corresponding to the difference between these two levels. The frequency of the emitted light can be found using the formula E = hν, where E is the energy difference, h is Planck's constant, and ν (nu) is the frequency of the photon.
Usually, transitions involving the lower numbered energy levels (e.g., n = 2 to n = 1) have more energy difference than transitions between higher numbered levels (e.g., n = 4 to n = 3). Therefore, among the options listed, transition from n = 4 to n = 5 would result in the light with the lowest frequency because it involves the smallest change in energy levels.