Final answer:
The constraint on an electron transition in an atom is that the energy absorbed or emitted must exactly match the energy difference between the two involved states, obeying energy conservation and quantum mechanical selection rules. These transitions correspond to quanta of energy, thus defining the wavelength of the photon absorbed or emitted. Allowed transitions are described by these selection rules based on principles of quantum mechanics.
Step-by-step explanation:
The constraint on the transition when an electron collides with an atom causing the atom to transition to a higher energy state is governed by the principle of energy conservation and quantum mechanics selection rules. When an electron absorbs energy from a photon, it can move to a higher energy orbit, causing the atom to enter an excited state. The electron can only transition to states where the energy absorbed is exactly equal to the difference in energy between the two states. Upon returning to the ground state, the electron releases this energy as a photon. This energy change is quantized, and each possible transition corresponds to a specific amount of energy, which in turn defines the wavelength of the emitted or absorbed photon. In hydrogen-like atoms, electromagnetic transitions must obey selection rules that stipulate which transitions are allowed or forbidden based on quantum mechanical principles.
For example, if an electron in a hydrogen atom needs to move from energy level 2 to energy level 3, it must absorb a photon with a frequency that corresponds to the energy difference between these levels. If an electron moves to a higher energy level by absorbing a photon, the energy of the atom increases. Conversely, when making a transition from a higher to a lower energy state, energy conservation occurs by emitting a photon with a frequency corresponding to the energy difference. The larger the value of n (principal quantum number) for the initial state, the longer the wavelength of the emitted photon will be when the electron transitions to the next lower energy level. Moreover, multi-electron atoms require consideration of additional effects such as electron repulsion and internal magnetic interactions for an accurate description of atomic transitions.