Energy Levels in Atoms

Electrons in an isolated atom (for example, an atom in a gas) can only exist in certain discrete energy levels. An electron cannot have an energy between these levels.The energies of the levels are negative. This is because zero energy is defined as the energy of an electron that has just been freed from the atom. Energy must be supplied to free a bound electron, so a bound electron has less than zero energy. The lowest, most negative level is the ground state. Higher levels are excited states. Energies are often given in electronvolts (1 eV = 1.60 × 10⁻¹⁹ J).An electron can move up to a higher level by absorbing exactly the right amount of energy, or drop to a lower level by emitting a photon. The photon's energy equals the difference between the two levels:ΔE = hf   or   ΔE = hc/λWorked example: in hydrogen, an electron drops from the −3.40 eV level to the −13.6 eV level. Find the wavelength of the photon emitted.
ΔE = 13.6 − 3.40 = 10.2 eV = 10.2 × 1.60 × 10⁻¹⁹ = 1.63 × 10⁻¹⁸ J
λ = hc/ΔE = (6.63 × 10⁻³⁴ × 3.00 × 10⁸) / 1.63 × 10⁻¹⁸ = 1.22 × 10⁻⁷ m (122 nm, ultraviolet)Because only certain energy differences exist, each element can emit and absorb photons of only certain specific wavelengths.