Final answer:
The wavelengths in the emission spectrum of an atom with allowed energy levels at 0.0 eV, 4.0 eV, and 6.0 eV correspond to the electromagnetic radiation emitted when electrons transition from higher to lower energy levels, with specific wavelengths for the transitions of 6.0 to 4.0 eV, 6.0 to 0.0 eV, and 4.0 to 0.0 eV.
Step-by-step explanation:
The given allowed energies of a simple atom are 0.0 eV, 4.0 eV, and 6.0 eV. To determine which wavelengths appear in the atom's emission spectrum, we need to consider the differences in energy between these levels, as these differences correspond to the energy of the emitted photons when an electron transitions from a higher energy level to a lower one. Using the relation E = hc/λ, where E is the energy of the photon, h is Planck's constant (6.626 x 10-34 m2 kg / s), c is the speed of light (3 x 108 m/s), and λ is the wavelength of the emitted photon, we can calculate the wavelengths associated with each possible transition.
For a transition from 6.0 eV to 4.0 eV, the energy of the emitted photon is 6.0 eV - 4.0 eV = 2.0 eV. This photon's wavelength can be calculated by converting the energy to joules (1 eV = 1.602 x 10-19 J), and then using the relation E = hc/λ to find the wavelength. Similar calculations can be made for transitions from 6.0 eV to 0.0 eV (6.0 eV) and 4.0 eV to 0.0 eV (4.0 eV), yielding three distinct wavelengths that correspond to the lines you would see in the emission spectrum.