Final answer:
An excited hydrogen atom can emit photons of specific wavelengths when it transitions from an excited state to a lower energy state. However, based on the given wavelength of 410 nm, we cannot determine the initial and final states of the hydrogen atom.
Step-by-step explanation:
An excited hydrogen atom can emit photons of specific wavelengths when it transitions from an excited state to a lower energy state. In this case, the hydrogen atom emits a photon of wavelength 410 nm. To determine the initial and final states of the hydrogen atom, we need to compare the given wavelength to known transitions in the hydrogen spectrum.
Based on the Lyman series, which is responsible for transitions from higher energy levels to the ground state, we find that the first five photons in this series have wavelengths of 121.6 nm, 102.6 nm, 97.3 nm, 95.0 nm, and 93.8 nm, respectively. Since the given wavelength of 410 nm does not match any of these values, it does not correspond to a transition within the Lyman series. Therefore, we cannot determine the initial and final states of the hydrogen atom based on the given information.