Final answer:
The frequency of radiation emitted when an electron in a hydrogen atom transitions from the (n-1)th level to the nth level is proportional to 1/n^2. This is based on Bohr's model, which states that the energy levels of a hydrogen atom are proportional to 1/n^2.
Step-by-step explanation:
The question asks about the frequency of radiation emitted when an electron in a hydrogen atom transitions from the (n-1)th level to the nth level, under the condition that n is much larger than 1. This scenario can be understood using Bohr's model of the hydrogen atom, which indicates that the energy levels in a hydrogen atom are proportional to 1/n2. When an electron transitions between these levels, the energy released corresponds to the difference in energy between the initial and final states.
Given that the frequency of the emitted radiation (ƒ) depends on this energy difference, we use the formula for the energy levels of a hydrogen atom (En = -13.6 eV / n2) to find the frequency. The frequency is proportional to the energy difference, which for large n is given by the change ΔE between the 1/n2 terms for the (n-1)th and nth levels. This results in a proportional relationship with 1/n3 because ΔE is proportional to the difference of the reciprocals of the squares of (n-1) and n, which simplifies to an approximate proportional relationship with 1/n2 for larger n, using the approximation that (n-1)2 is approximately n2 for large n.
Therefore, the correct answer to the question is that the frequency of radiation emitted is proportional to 1/n2, making the correct answer (c) 1/n2.