In order to determine the wavelengths of the photons emitted during the de-excitation process, we need to know the specific element under consideration. Different elements have different energy levels and transitions, resulting in different wavelengths of emitted photons.

However, we can discuss the general process of de-excitation and the associated energy levels. When an atom or nucleus is in an excited state, it means that one or more of its electrons (in the case of the atom) or nucleons (in the case of the nucleus) have transitioned to higher energy levels. These higher energy levels are unstable and tend to spontaneously decay back to their lower energy levels.

During the de-excitation process, the excess energy is released in the form of a photon. The energy of the emitted photon is equal to the energy difference between the initial excited state and the final lower energy state. The energy difference determines the wavelength of the emitted photon through the relation:

E = h*c/λ

where E is the energy of the photon, h is Planck's constant, c is the speed of light, and λ is the wavelength of the photon.

To determine the specific wavelengths emitted during de-excitation, we need to refer to the energy level diagram or energy transition tables for the given element. These tables provide information about the energy levels and transitions specific to each element.

For example, in hydrogen, the Balmer series corresponds to the de-excitation of the electron from higher energy levels to the second energy level (n=2). The wavelengths of the emitted photons in the Balmer series can be calculated using the Rydberg formula:

1/λ = R*(1/2^2 - 1/n^2)

where R is the Rydberg constant and n is the principal quantum number of the final energy level.

In conclusion, to determine the exact wavelengths of photons emitted during de-excitation, we need to know the specific element and refer to its energy level diagram or energy transition tables.