According to the quantum-mechanical model for the hydrogen atom, which electron transitions produces light with the longer wavelength: 2p→1s or 3p→1s?

2p→1s

Explanation:

Frequency is inversely proportional to wavelength. The higher the frequency, the shorter that wavelength. The smaller the frequency the longer the wavelength. The frequency of light associated with 2p→1s is less than the frequency of light associated with 3p→1s since the latter represents transition from a much higher energy level. It follows that the wavelength associated with the former will be longer since its frequency is lesser. This deduction follows from our argument about the inverse relationship between frequency and wavelength.