An electron can move up to a higher energy level if it gains exactly the right amount of energy. This is called excitation, and it can happen in two ways.1. Absorbing a photon. A photon is only absorbed if its energy exactly equals the difference between two energy levels. A photon with any other energy is not absorbed, because a photon cannot give up only part of its energy.2. Collision with a free electron. A fast-moving electron colliding with an atom can transfer some of its kinetic energy to an atomic electron. The incoming electron only needs at least as much energy as the gap; any extra is kept as kinetic energy.
Excited states are unstable. The electron soon falls back to a lower level. This is de-excitation, and each fall releases one photon whose energy equals the difference between the levels:hf = E1 − E2 where E1 is the higher level and E2 is the lower level.Worked exampleIn hydrogen, an electron falls from the n = 3 level (−1.51 eV) to the n = 2 level (−3.40 eV). Find the wavelength of the photon emitted.ΔE = −1.51 − (−3.40) = 1.89 eV = 1.89 × 1.60 × 10-19 = 3.024 × 10-19 Jλ = hc / ΔE = (6.63 × 10-34 × 3.00 × 108) ÷ 3.024 × 10-19 = 6.58 × 10-7 m, which is 658 nm (red light)A larger energy gap gives a photon of higher frequency and shorter wavelength.
Excited states are unstable. The electron soon falls back to a lower level. This is de-excitation, and each fall releases one photon whose energy equals the difference between the levels: